For those of you who may not have a full understanding of what Anatta means, within Buddhism they have what is called Three Characteristics of Life. There is Dukkha, unsatisfactoriness, that is one of the Characteristics of Life. Everywhere we see things are unsatisfactory. We have impermanence, the Pali word is Anicca. Impermanence is the second, everywhere we look things are changing, it is pretty clearly a characteristic of existence.
Then Buddhism has a third one, in Pali called Anatta. Translating it into English is not so easy. Some people use the word non-self, some people use not-self, those two have slightly different meanings, some people will talk about voidness, emptiness, all sorts of other words in this way. Non-ownership is another way to express it, we don't own anything.
Anatta, the second part of the word, "Atta", basically means self, but it means a big self, like an eternal, it is hard for me to explain, because I really don't use that term, but that is what "Atta" basically means, a self, an eternal, everlasting self. Now some philosophies teach that we as little tiny self's will one day when we become enlightened merge in the big self - Atta - that was the teaching at the time of the Buddha and it is still the basic teaching of Yoga philosophy. That there is this Atta, that we all, when we get enlightened, merge into it. It is not unsimilar to the God theory, except that a Jew or Christian believe you don't actually merge with God, you go there and live with him happily ever after. So this Atta was meaning a self, an eternal self. The Buddha taught Anatta, which is the opposite. He basically said here was no eternal self, there was no big thing that we will merge into.
Now you can't prove this. Only an enlightened person actually knows for themselves, they experience it on a deep experiential level, for everyone else it stays a theoretical teaching within Buddhism. On a practical level the term non-ownership helps here. Do you actually own you body? If you could, then you could command it never to get ill, never to get injured, never to grow old, no wrinkles, no grey hair, nothing. If you owned it, you could control it. You can't control the body, ultimately it is not yours. You don't own it, there is a non-ownership quality with the body. That is pretty easy to see because the body of everyone just dies.
On that level it is a bit of an experiential understanding. Still, as much as we can understand that, most people don't believe it, they tend to believe this is me, my body. Me, me, mine, mine. When you are in the meditation practice, say you are sitting there trying to be aware of your breath, is it a man's breath or a women's breath? Is it 23 year olds, is it 49 year olds, is it a dark skinned person, light skinned? During these moments when we are meditating there is no real "me."
You are being aware of the breath, there is just breath, there is no man breath, female breath, there is no old breath or young breath, it is just breath. And there is no "me, me, mine, mine". You can experience that, that there is a moment with no "me". Anatta is kind of present in an odd way, and the same thing can happen when you grab a door. If you are actually mindful when the hand grabs the door and you feel the door, there is just sensation right there with your hand grabbing the door, that's all that is happening, it is a physical sensation. When you walk just being aware of the feet stepping, stepping, the pressure on the bottom of your feet or whatever, there is no real "me, me, mine, mine" present. There is just sensation present. These are moments when you don't have the thought of "me" in the mind.
As to when we start thinking and wandering and carrying on, can you own your thoughts? If you could, you could control them. We are trying to control them, but to a certain extent we are actually trying to just let go of them and not attach to them. So with our thoughts we are trying to be aware that they are not really "me", they are not really "mine". They are just coming and going. Do you have any thought which is absolutely original? Nobody else on the entire planet has had that thought? It is impossible for you to have a thought that is totally original, because every word that is going on in your head someone gave to you. Every picture that you had in your mind was a sight that you saw somewhere else. So everything you formulate is not original, it is based on conditions. It is based on what you heard, what you saw, what you tasted, what you smelled, what your touched - your sense doors. Everything you know is conditional. So every thought that you have is based on something else, therefore it doesn't exist in itself as an entity, as a self.
Now, I could go on in this way, maybe you are getting the idea, Anatta is not something we can actually prove, but what we are trying to experience, trying to understand, that there is no permanent, unchanging self here, that is what we are doing with the practice. The more moments that we are not attached to "me, me", then the more moments we are actually experiencing that there is no permanent, unchanging "me".
Maybe through lack of imagination, maybe there is something else in-between Anatta and Atta, but that is also something we are going to experience if we get enlightened. That will be something we prove in the end. There can only be one ultimate truth. Whether it is found in Buddhism, whether it is found somewhere else, there are words in the Bible from Jesus that say, "The pure in heart will see God," and Buddhism says, if you purify you'll get enlightened. There is no real difference between these two statements, as to the ultimate nature of them. If you purify you become enlightened, you will see whatever there is of the ultimate truth. So the question then becomes not so much the intellectual side, but how do we purify? How do we actually do the work in order to get to that point that we then understand what these theoretical words mean.