Sauron was not a great eye in the books. He had regained his formed and could walk. Gollum himself saw the Dark Lord. He even commented that he has only 4 fingers.
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Nardor is the greatest work of fan fiction the world has ever seen
The film version of things is obviously and probably deliberately inaccurate. It was done for effect most likely. I think the 'Red lidless eye' was what people saw when they looked into the Palantir and found Sauron? Or maybe this was the image Sauron could project of himself. In The Silmarillion it says:
"There he took up again his great Ring in Barad-dûr, and dwelt there, dark and silent, until he wrought himself a new guise, an image of malice and hatred made visible; and the Eye of Sauron the Terrible few could endure." The Silmarillion
One thoery is that the Eye refers to Sauron searching in the Palantir. I've also noticed this quote:
"'Easy it is now to guess how quickly the roving eye of Saruman was trapped and held; and how ever since he has been persuaded from afar, and daunted when persuasion would not serve."
Is this a general use of the word 'eye' or is there more to it?
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Utúlie'n aurë! Aiya Eldalië ar Atanatári, utúlie'n aurë! Auta i lómë! Aurë entuluva!