I like the idea of this thread, though it's kind of vague. So, I'll try to answer your question as best as possible.
To start, I have only met a couple of people that I believe even begin to understand the way I work upstairs. Don't get me wrong - this isn't about genius or thinking on a higher level than other people: My brain is just not wired the same. At some times I'll understand something that no one else does and it's like adding two and two for me, and other times I feel like I'm the only one who's completely lost.
Things like Math and Science come easy; I just "get it." I can't explain it any better than that. But with social matters it all seems so arbitrary. I have absolutely no idea what I'm doing most of the time, so I try to shun that sort of thing. I can mimic basic social techniques, but when paired with someone I don't know I usually freeze with a nervous grin on my face. Believe me, it's not the least bit charming. Sometimes I wonder whether it's my inclination towards introspection and avoidance of anything social that makes me awkward due to lack of experience, or if my awkwardness drove me to introversion. Then again, I have never been that strong in E to begin with.
I'm very disorganized, and very forgetful. My thoughts, my room, everything about me is pretty messy, even sometimes lazy. Especially when stressed or depressed, I tend to take a "I don't give a damn" or "I'll do it sometime later" approach to things around me. Because of this I sometimes drop everything, avoiding responsibility.
I don't know if this is how other INTPs work, but I'm also very musically inclined. Music is one of the few things that seems to actually make me feel strong emotion. My mind's like an iPod perpetually on shuffle; there's never not some tune playing in my head, even while I'm thinking in depth. It's very entertaining, actually.
Sigh. The only thing worse than being an INTP is a female INTP. (Or I suppose an INTJ. Or a female INTJ...)