My Open University course has started with an interesting discussion about the Self. Am I the same person I was as a child? What makes me that person over time?
Locke thought that memory was essential to the linkage, but that memory did not have to be stored in one bodily location.
Using thought experiments such as a drunk man getting into a fight and not remembering his violent action Locke thought that by not remembering the drunk could not be held responsible for his actions.
This is not my viewpoint. The person is more than just a series of memories. Personal identity has to include consciousness and all actions whether we are conscious of them later on or not
The transitory nature of personal identity is set out by Thomas Reid who put forward the idea that if a child (A) was flogged for scrumping apples and later in life (B) reclaimed the standard from the enemy and subsequently was (C) promoted to general; then if B could remember A and C could remember B, but C could not recall A, it would be illogical to state that A is not the same person as C. A=B and B=C therefore A=C.