[Several posts disappeared from the "finding yourself in other people's dreams" thread, apparently due to forum software issues. The following thoughts are excepted from the last one.]
I speculate that your dream characters, which are related to aspects of your own personality, amount to a sort of 'address' in a larger collective mental space. And then they also exhibit characteristics reflected from that collective place where you are putting your attention.
Using a math example again (I'll stop with these if you tell me they never help), there's a model of elliptic geometry in which two points on the opposite side of a spherical shell are regarded as the same point. Years ago, the night after learning of this idea that is like something being two places at once, I dreamed of a fiery bus crash at my 'antipodal point'. A bus was destroyed by a missle in Serbia that same night (or day, in Serbia). That was perhaps my first premonition of that type, though at the time it could have plausibly been a 'coincidence'. (I hate that word coincidence by the way. Its almost always used to imply meaninglessness or randomness, as if coincidences are by nature that way. But that judgment is not in the literal meaning of the word, and the skeptical connotation deprives us of what is otherwise the right word for the experience.) I don't think that the 'antipodal point' idea was very relevant to understanding what happened, it just opened my mind to a possibility and directed my attention in that way.
Similarly, I think our thoughts direct our attention to other places, so to speak, that are like our thoughts. When we form the thoughts, there are elements of both creativity and discovery. We're 'making' the thoughts and also moving our attention. People who emphasize the individual aspect of that regard it to be in their own minds, and they believe they have active control over their private experiences depending on the extent to which their thought of themselves includes creative power. People who's thought of identity includes a collective component imagine the experience to be shared. Of those people, the ones who strongly emphasize the creative part regard all physical objects and events to be a manifestation of thought. People who exclusively emphasize the 'witnessing' part regard it all as an expression of God or nature, and we're just along for the ride. These different thoughts of awareness and power directly change our interpretations of our experiences. They alter the collective, objective aspects of the experiences also, but that effect is subtle because of logical limitations and collective inertia. Even who we are individually is to a large degree collective: we share a common genome for instance, and much else.
Why don't people's thoughts of such things accurately reflect their real power? I think that to a significant extent they do, but people try to avoid acknowledging things that they don't want to be responsible for, and that has some effect on their real power. Also, people just have different preferences about how they want to be. Since were all scavenger/predators, its painful to be emotionally genuine in relation to the people and animals we prey on. So we run away from ourselves, which changes what we are, just like anything else we do with our creative attention. Thus we make ourselves into what we are, as constrained by the fact that only ways of being that work can continue to exist. And so for a time we have no other way to live.
An obvious implication here, is that when confronted by strange dream characters, you can become more aware of them as parts of yourself, or as parts of other people, depending on how you direct your attention.
Also, the New Age idea that reality is a manifestation of thought has truth in it, but only sort of. The full reality is more than those thoughts, which are also interactive reflections of the reality. I think this was the meaning of my muse when he said "you claimed to have created me".
See also my last post in the 'past lives' thread for a related thought.
As an unrelated side note, the reason I never "like" anyone's posts isn't because I don't like anything, but because I don't care for the control that Facebook's "like" patents give them over information. It doesn't just signal our approval to other DreamViews readers, it also is organized into a big global database, where we're profiled for advertisers and government security agencies, as governed by policies that are ostensibly innocuous but not entirely public. I don't mind if you "like" my posts, it makes me feel good actually. And maybe I'll give up my doomed resistance to Facebook, Google, etc. and start "liking" things also. I just want people to know that they shouldn't interpret my past pattern as a sign of withheld approval.