Ah, I stand corrected. Well, as far as the self goes, that unifying factor is consciousness. Without it, which is quite impossible as we are it, we would be really just a lump of incoherent mental beeps and bloops. In that sense I view Buddhism as the most radical form of Advaita -- it tells absolutely nothing about the nature of enlightenment, everyone is forced to come to their respective "aha!" moment. Also, when you look at doctrine of "atman" in Hinduism, you will see that it does not actually presuppose a personal soul. It only says that from which we derive our of sense of self (Atman) is the absolute consciousness (Brahman). But of course, if one spells out that there is Atman and Brahman people are inclined to search for it in their perceptual field. Hence Buddhism as reformation of Hinduism (and its attempt at bypassing the trap of objectivization of self).