Years ago, I knew a computer programmer by the name of Barry. At the time, he was very fond of a particular PowerBook Duo. He took it on business trips around the world. From time to time a key would break, or a hinge would snap, and he would replace or repair the part. Eventually, he figured he’d replaced every part at least once.
He affectionately referred to it as still the same computer, saying that at any one time there were parts from the previous version of the machine, stretching back to when he first bought it however many years previous
Was Barry right?
If you are disinclined to think that he actually had the same computer the whole time, I encourage you to think about why you think so. But keep in mind that much seems to be the same of us. You have likely next to no atoms from your original stock, however defined (e.g., you at birth, you at conception, etc.). On the other hand, if you agree that Barry kept the same computer all those years, try to think through what might underlie that continuity, and again apply the same reasoning to us.
Finally, as an interesting twist on a more personal note, my father, now in his mid-70s, has a tiny amount of scar tissue on his neck. This is a result from an injury he suffered as a teenager. So there is a very bizarre form of continuity over time here for sure!
Fields to consider: metaphysics of persistence and identity; mereology; legal responsibility and powers-of-attorney; biochemistry.