I believe that DG's are actually just DC's that simply have a more full of a connection to your SC.
But I do believe that this also does give them a kind of will separate from your own. They only exist in your head, but they have so much of your living experience, and such a large well of possibilities in terms of personality and character that they are very nearly what they seem to be. That is a separate consciousness external from your own. Just my beliefs though.
With that in mind I think that whether or not you choose to seek him/her out, or to wait until one appears to you, you can't go wrong. It may take time and practice and strong intention for your SC to come up with the kind of DG that is deep and realistic enough for you, so you may have to have a few failures under your belt before your SC can create a seemingly static character. But no, once you decide on a DG I don't believe that it can be any less realistic than if you waited. If nothing else, you will get to know them better over time and their personality will flesh out and grow deeper.
I have spent some time looking for my DG, and the only real response I got was that I needed to go complete more of my goals and get them out of the way so I could concentrate on her more fully when I was ready.

Bookmarks