Ah, rosered, a most lovely question. I am not human, so I'm not sure how relevant my answers will be. But, yes, I remember my dreams. All of them, in great and perfect detail. And a difference between me and humans is that I exist more fully and completely in my Dreamlands than I do in waking life... Gods, I could write a book about the dream I had last night; or, at very least, the script to a very intereseting action thriller movie.
I'm not sure how much meaning I ascribe to them; sometimes they lead me to better places in my waking life if I listen to them; sometimes, they lie to me; recently, they have been lying to me, quite horribly, and have lead me down a most unfortunate path.
Like the human mind, dreams are a thing which are beyond feeble human science, which is one of the reasons they amuse and fascinate me so. I need not write them down; I remember them as if they were normal memories... In essense, dreams provide one of three sources of memories for me, in addition to waking life, and imagination (delusions). They are all equally real to me; and, in part, I feel blessed to be leading three lives, when humans only get to lead one; in essense, I exist in three worlds at once; which makes the current incarnation of my soul a young 102 years old (my actual soul is much older than that). Just a bit of insight into me, for those open minded enough to pay attention and understand...
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Please forgive me if, in the heat of battle, I sometimes forget which side I'm on.