For me, the open/honest sharing of thoughts is the ultimate intimacy. If you let me see yours, I feel deeply honored and very close to you -- I feel like you trust me and are giving me the opportunity to know/love you (which feels to me like the greatest gift one can give). And if you seek out mine, I feel deeply valued and loved. So livejournal is a tool for something that almost never happens in face-to-face interactions. Most of you, even, would feel quite awkward if confronted with "what are you thinking?" in a face-to-face interaction but here, you share it with me. And even more so, most people would hesitate to ask me my thoughts, but when I offer them freely you can trust that I do want to share them. And just knowing that you read what I share (whether you comment or not) makes me feel understood and incredibly valued by you.
For me, how much I love a person is directly proportional to how much I think about them. If I love you, I think on your words and your movements and every little thing I know about you. If I love you very much, I think about you all the time and constantly check your online homespaces to see if you have shared something (though it's less if you don't share often). Because this is such an automatic consequence of love for me, I interpret it as love from others as well.
And the highest expression of this is, for me, when you take my thoughts into your mind and reshape them to become your own. Whether this is in the form of "oh wow, I agree!" or "ohh, that makes me think of this opposite/semi-related thing," it makes me feel as if you just flung wide the door of your heart and pulled me in with gleeful excitement. I'm thinking right now of some posts I made that sparked posts which disagreed entirely with my original post and they gave me that same feeling of honor and acceptance and love (although they didn't give me the thrill of connateness like agreement ones do ;-)). Conversation can do this, but reading/writing does it even more because it means you spent your time seeking my thoughts even without the impetus of me being there to invite/spur you.
*"Bel" has been used mostly by those who have sought my thoughts and shared theirs with me -- while it started as just an expression of affection, it now stands as a reminder that those who call me that have thought-intimacy with me. When those who do not have that intimacy with me use it, it feels like a stranger calling me their lover -- wrong because it is untrue. (the only exceptions to that are with people who feel like kin without them reading my LJ -- it happens very rarely but it has happened) I experimented with introducing myself as Bel last year and as a result, had lots of strangers calling me Bel. It felt so wrong that I started disassociating with the name and it was making me uncomfortable until recently, when Anita and Chip called me by it and I began to feel the truth of it again. And G (the toddler) called me Bel when adults were calling me Bel and James pretty equally, and that made me feel the truth of it too (that kid sees things to an almost intimidating level). I really can't express the sense of relief I feel at having my name feel true again.