7 Why We Suffer
WHEN WE LOOK deeply at the nature of things, we see that in fact everything is impermanent. Nothing exists as a permanent entity; everything changes. It is said that we cannot step into the same river twice. If we look for a single, permanent entity in a river, we will not find it. The same is true of our physical body. There is no such thing as a self, no absolute, permanent entity to be found in the element we call "body." In our ignorance we believe that there is a permanent entity in us, and our pain and suffering manifest on the basis of that ignorance. If we touch deeply the nonself nature in us, we can get out of that suffering.
Your nature still exists even if it is temporary. You can still swim in a river even though it changes constantly. Accepting the impermanence of self and others doesn't create any of the difficulties you're imagining.
If I write you a letter, do I address it to the you who is upstream, or the one downstream?
I think the point is, not that we are completely different people, one moment to the next, but that we should embrace change rather than fight it. Life and the world around us is constantly changing and we are better off for changing with it.
Re your hypothetical letter, you can only address it to the persona you last knew, so to speak. Upon renewed communication, you'll learn how that person has changed, and maybe you will too a little or a lot.