The Problem of Personal Identity - Why it Matters (with a note on Descartes)

In Philosophy of Mind, there is a problem called "the problem of personal identity." How is it that "I" am the same person through time though every seven years, my body is made up of completely different matter? Descartes (and probably all/most of dualists) says that personal identity is found in the unchanging non-extended, indestructible mind/soul/spirit. This thinking thing is ontologically (ontology has to do with being of the nature of a thing) distinct from body and are radically different substances.

The problem with Descartes attempt to solve the problem of identity is "the interaction problem." How does the body and mind interact with each other if they are causally distinct. Other philosophers have given numerous answers from answering yes, no and maybe to trying to redefine the problem and/or becoming monists (the belief that human beings are composed of only one substance. Hegel, Berkeley, Leibniz, Spinoza, Dawkins, Hitchens, Nagel are some monists.) A second problem for Descartes is that it makes personal identity irrelevent to the body. This can be understood as a sub-problem of the interaction problem. If the mind and body are distinct from each other, isn't personal identity then irrelevent for the body? What is the connection? Hence: the interaction problem.

Why does this matter? 1. Descartes brought about David Hume who brought Kant and Hegel who brought about Kierkegaard, Nietzsche and Marx who brought communism, socialism, existentialism and a bunch of other fun things that cause problems and solve problems. 2. I am being tested over this is about 2 hours. 3. It shows how finite we are. Whatever answer we give, it automatically restricts us to a certain view which seems to inevitably brings about problems.

In conclusion, do you agree with the picture?