Excellent post.

I have pondered the same sort of questions. Here is an excerpt from my 2009 book.

My father is 88 years old and a devout Christian. Before he became afflicted with Alzheimer’s he expected to have an afterlife where he would be reunited with his deceased daughter and other departed loved ones. He doesn’t talk of this now and would not be able to comprehend the question if asked. He is now almost totally unaware of who he is or what his life was. I sometimes tell him the story of his life, details of what he did in his working life, stories of his friends, the adventures he undertook. Sometimes these accounts stir distant memories. I have recently come to understand that there is more of ‘him’ alive in me then there is in him. When he dies and were he to enter the afterlife in his present state and be reunited with my sister he would not recognize or remember her. Would he be restored to some state earlier in his life? Would he be the same person at all?

I originally wrote this to illustrate problems with the religious idea of resurrection. I now believe that this problem of identity is common to all complex evolving systems including 'ourselves'. For example species evolve over their lifetime and although we intuitively know that we are identifying something distinct when we name a species such as homo-sapiens the exact nature of the distinction is slippery. The debate in biology over the definition of species has been long, heated and unresolved. Some definition referring to species are attempts along the line of interbreeding populations that do not overlap with other populations. However this is a leaky definition. For example it has recently been found that modern human populations contain some Neanderthal DNA. Our 'species' interbred in the past, should we still be considered separate species?