But their personalities are so similar - they feel like they are small people, not really worthy of messing with the high powers of the universe.
George is trying not to have dreams because they might end up changing the world, and he doesn't believe he should have the right to change things as they are.
Alder is trying not to have dreams so that he isn't pulled over the low stone wall in the Dry Land and let all the dead that cry out to him loose, or pull him over the wall with them.
Both of them don't believe they are "big" enough people in their worlds to be meddling with such world-altering affairs.
Both of them are very quiet, almost shy men, very humble and heartfully honest. To use this character twice in her books, i wonder who she is refering to ... or if she is refering to herself? Has it ever been known whether she has had dreams that she wished not to have? So much that she had tried to escape them by any method available to her?
George with his illegal use of the drug-cards, Alder with little Tug, the kitten. And then if you remember Ged as well was pulled back into his body by the touch of the little Otak, but that wasn't really sleep ... just a parallel reference.
And in one of George's dreams he sees an Alder tree. A little bit of a stretch, but you never know ... maybe she wanted a 'George' in "The Other Wind" and came across the word 'Alder' when she was re-reading through "The Lathe of Heaven" and came across the word, as i did, and thought, "That'd be a perfect name!"