What is a self?? I propose that it is the same kind of thing as a center of gravity, an abstraction that is, in spite of its abstractness, tightly coupled to the physical world. You, like every other material object, have a center of gravity (or more properly a center of mass, but we’ll ignore that nicety here). If you are top-heavy, your center of gravity is higher than average for people of your height, you have to work harder to stay upright, and so forth. There are many ways of locating your center of gravity, which, depending on such factors as the shoes you have on and when you last ate a meal, moves around in a smallish area in the middle of your body. It is a mathematical point, not an atom or molecule. The center of gravity of a length of steel pipe is not made of steel and indeed is not made of anything. It is a point in space, the point on the midline running through the center of the pipe that is equidistant from the ends (roughly, depending on imperfections, etc.). The concept of a center of gravity is a very useful thinking tool in its own right. In effect it averages over all the gravitational attractions between every particle of matter in a thing and every particle of matter on the planet, and tells us that we can boil all that down to two points—the center of the earth (its center of gravity) and the center of gravity of the thing—and calculate the behavior of the thing under varying conditions. For instance, if a thing’s center of gravity at any time falls outside all the points of its supporting base, it will topple. What you are is that rolling sum of experience and talent, solemn intention and daydreaming fantasy, bound together in one brain and body and called by a given name. The idea that there is, in addition, a special indissoluble nugget of you, or ego, or spirit, or soul, is an attractive fantasy, but nothing that we need in order to make sense of people, their dreams and hopes, their heroism and their sins.
Philosopher Daniel Dennett's Book Intuition Pumps