Most likely most people here would agree that if you make an exact copy of a person's brain, whilst leaving the original intact, it would be a new person, identical but divergent from the original. A new thread of consciousness by such definition.
But then, what if you destroy the original at the moment of copy? It would appear to the same.
But then, what if you replace each neuron one at a time over a period, maintaining the original network? This question is troubling because it brings into obvious doubt the integrity of our notion of consciousness. As it is in fact the case that we shed most of the atomic matter that constitutes us in a given year, we are clearly immaterial. Patterns.
So put plainly: should you copy your brain all at once, killing the original, are you a new person? But if you are: transitioning slowly piece by piece over time, which is what we observe in nature, this maintains the conscious strain? How are these different?
It's obvious to me there is something fundamental here we are missing. I welcome any insights you all might have had in similar thought experiments.