Not self has been my favorite entry door into mindfulness practice. I know it is different for everyone. Others connect more with the characteristic of suffering. And yet others use impermanence as their primary source of insight.
Today, sitting in the midst of turbulences, I could see clearly the importance of bringing the mind back over and over again on the immediate experience of breath, and unpleasantness, and aversion. Not adding more suffering with extra thoughts about 'I'. Eventually, mind grew more calm.
Ayya Khema has this to say about not self, or rather corelessness as she calls it:
"Why are we practicing? To find freedom within. Our lack of freedom arises because there is pressure, stress, dissatisfaction, wishes, hopes, plans. There is the idea of becoming different from what one is. All these ideas put pressure on ourselves and we often (mistakenly) think that pressure comes from outside. We can never come to the end of our desires. They keep on arising. But we can come to an end of desires by first reducing, and then eliminating them. The self as we ordinarily see it is like an onion. Try to peel off the identifications. See who I think I am. See what's left after peeling off. See that there is someone that knows what's left after peeling off 15, 16 identifications. Who is this knower? Usually the last bastion that we hang on to, that is totally unreliable. That knower most often knows nothing, or knows the wrong thing, or is very unreliable. Where is this knower? Certainly not in the big toe . . . Most likely in the mind. Does it have a definite seat there? Does it have a solid entity or is it a mental formation? We cannot say who knows, but what knows. We make up an image that we call me. How did we get the idea that this thing that's sitting on the pillow that's the body is called me. That's a mental formation. Why would we want to change that mental formation? Because we notice 'me' is the source of all our problems. No 'I', no problem."
An ongoing process of dis-identification. Letting go of the compulsion of mind to form self-thoughts.