Our narrator is plagued with insomnia, and he has a pretty fascinating way of describing it:
Everything is so far away, a copy of a copy of a copy. The insomnia distance of everything, you can't touch anything and nothing can touch you. (2.56)
Our narrator has distanced himself from reality, that's no surprise. The obvious consequence is that he doesn't even realize that he is Tyler Durden—that it's been him peeing in soups, splicing porn into movies, and starting fight clubs across the country. But when he asks himself, "Am I asleep? Have I slept?" (12.56), he doesn't realize that he's also sleepwalking through his daytime life. Even though our narrator isn't asleep, he's totally tuned out to what's really going on.