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Ship of theseus and continuity of death.
Continuity of death. You are alive when you exist. You are dead when you don't. I think it's useful to think that a fraction of you can exist. Consider the 5 year old me. I am a very different person now and have very few memories remaining from that time. A large fraction of that 5 year old no longer exists. But some of it is still part of me. The graph of a fraction of present me that existed and will exist may be modeled as a gaussian, where the horizontal axis is time, centered on present (clamped by the beginning and end of life). How wide is that gaussian? Depends on how good my memory is. Better memory = wider gaussian.
Here are some related thoughts with low epistemic status.
Ship of theseus. Suppose that the ship of theseus consists of both the structure and the atoms that make it up. By the end of the journey the structure remains but the atoms are gone. So the original ship is partially "dead". The final ship and the original ship are partially the same. The resolution of the paradox is to think of existence as a continuous quantity.
Akrasia. The width of the gaussian may be related to the severity of akrasia. Future me is only partially present me. The less of me the future me contains the less I am willing to work for his benefit. This seems testable. Is there a correlation between memory and akrasia?
Immortality through brain uploading/cloning. Step change from my existence to the existence of my clone is scary. Continous change is not as scary. It's closer to the natural process of changing over time.