the self does not exist and you are the universe
The self is really a trick our mind plays on itself. If you try to examine where it is, you will see that there is nothing there. You might think the self is in your brain or mind. Try to pin down where that is physically. We often think of where "we" are from the viewpoint of our eyes. Is the self behind the eyes? Maybe it is the electrons buzzing around the brain in neural impulses. Imagine those electrons were recorded and played back exactly in an equivalent electronic circuit you could hold in hand or place on a table. Surely that cannot be the self. And so you begin to see that there is nothing there, its a trick, an illusion. But then what is perceiving that there is nothing there? Surely that must be the self. Aha, now we're onto something. But then where is that? You can keep playing this game ad infinitum.
I want to know the I that knows me when I know that I know that I know.
The mind cannot know itself just as the knife cannot cut itself. Breaking this down further, there are two kinds of self, both of which are convenient tools for easing our language and survival.
the fabricated self
The first is known as the fabricated self. The fabricated self is the sum of all the stories and experiences others put upon the individual. This is quite useful in a civilized society and allows a person's reputation to help or hurt their interactions with the rest of the group. This tool protects the group from weirdos but also saves time and interactions can move beyond purely introductions and back story. However, these stories and perceptions then impact how the individual also views themselves. This distracts them from who they really are. We tend to reinforce the fabricated self and avoid those things that go against our personal narrative. This limits personal development and is not conducive to our happiness.
You're under no obligation to be the same person you were five minutes ago.
We need to drop the the story and truly interact with others as we are not as who we pretend to be. It is only a that, a fabrication.
the innate self
The other kind of self is the innate self. This can be experienced as a sense of self preservation under situations of survival. The compulsion to return to safety is automatic. It is an ancient drive from the oldest reaches of our brain lashing out reflexively in a fit of self preservation. The brain is hardwired to preserve its physical body in order to keep on living. This is an extremely useful tool biologically, the automatic action and reflexes of keeping the body secure is a huge burden lifted from the conscious mind. If we accidentally touch a hot stove, our hand jolts back immediately upon sensing the heat. This is the innate self acting on our behalf. We do not feel the heat in our finger, notice the sensation, notice the pain forming, consider our options and then act. That's far too slow to preserve our fingers, there's no time for that!
The innate self acts swiftly before our mindful consideration can step in. This is the issue many Buddhists see with this aspect of the self, the point is to consider; in what other aspects of your life are you acting automatically? Or where else are you at the mercy of this arcane twitch? In modern everyday life, we do not often need to utilize the innate self for survival. We are for the most part safe to go about our daily lives. And so the innate self runs rampant, utterly bored, and finds new things to "save" you from. It might be gossip from a coworker, a glance from a stranger, and other harmless things like an email from your boss (it is just text on a screen after all).
the sort of third kind of self
So the self is actually a collection of stories, and our biological preservation instinct, but we can't pin it down locally. But surely it must exist somewhere. I sure feel like me! The self most people are familiar with is a nebulous emotionally bounded me. With another kind of self that is my physical body: the gray matter housed in a skeleton driving a meatsuit that you look out from everyday.
What we commonly think of as our "self" is constantly changing. We feel as if it is a constant thing because the experience of life is continuous. Our attitudes, opinions and emotions change with time. We learn, mature (its not a phase mom!), and age, all by varying degrees across time. Not only is the emotional self changing but also the physical body. Our bodies change constantly like the ship of Theseus. Our cells are constantly growing and replacing old ones. Even the boundary of our bodies is unclear, our hair and top layer of skin are just dead cells, that cannot be a part of "me". Our pores and lungs exchange air and moisture with the environment. Should those molecules be considered part of "me"? And how far away from my skin is the boundary? A mile or a micron? Those molecules are always moving and crossing the boundary. And even if we could create a consistent spatial boundary, our bodies still change with time and we age.
no-self
So the fabricated self, innate self, and the emotional self cannot be located physically nor are consistent in time. Our bodies are not constant in time and even the boundary is unclear. This is the concept of no-self. There is nothing inherently 'you'.
At first this may seem like nihilism and imply that everything is devoid of value. Consider what's being referred to when people say "I am so proud of you", or, "you make me happy". Well you does not exist. Bah hum bug. Any role model, or idealistic image (bravery, Christ, the Buddha) is just a trick your mind plays for its own convenience. Everything that we assume to have an essence is actually empty. Now that is bleak.
However, no-self is not part of a nihilist view, it's quite the opposite. It should be viewed as: if everything is empty or devoid of its own essence then there can be no differentiation. Everything is the same thing. As there is no 'self' there can be no 'other selves'. There is no difference between you, your neighbor, a tree, or the entire cosmos.
By labeling a group, me/self/I, immediately another group is created of things that are not that, and they are excluded. This is the key issue with clinging to the self. We see our 'self' as a separate entity from all other things. We see our 'self' as a thing in the world, not of the world. But there is no self, only no-self. You and everyone else are not separate beings, we are all part of the tree of life and of the same cosmos. A wave is part of the ocean the same way people are of the universe. This is why Buddhism denies the self, it reminds us of the oneness present in the world and to have compassion for all things.
With this viewpoint, we can translate the earlier saying. "You make me happy" really means "isn't it great to be alive".
No-self shows us that everything is one and the same. You are the universe.
No-self shows us that none is the same as one.