Zarpaulus wrote:

There's a massive difference between losing a part of you and losing all of you.

I may have overreacted a tad there, sorry. Nonetheless, the point remains that there is no particular part of the brain that is irreplaceable through ordinary means, and so replacing them through artificial means must be possible without loss of self.

Zarpaulus wrote:

Also, what about epigenetics? That's just selectively coiling or uncoiling sections of the strand by attaching or removing tags.

Firstly, because those tags are attached, and so can be considered a part of the DNA strand – whether they are or not is a matter of convention. In that case, removal or addition of a epigenetic tag would be the equivalent of altering the DNA strand. Secondly, epigenetics are vital for determining cell identity. It's those tags which determine how long the DNA strand remains in the body, what the DNA does.... everything. If you alter the tags... which occurs naturally to control protein expression iirc... then you alter DNA expression, at which point another aspect of the paradox applies: If you take the planks of the Ship of Theseus and use them to build a cabin so that every part of the ship is present in the construction, is the cabin then the Ship of Theseus? That is, if you alter a DNA strand's expression, does it remain the same strand?

Zarpaulus wrote:

Something else you might find interesting, each cell has roughly half the same DNA atoms as its parent cell had, and half of all cells have a strand that was originally in their "grandparent" cell, and so on and so forth.

More interesting is the corollary; there are at most 2 cells in your entire body that contain your “original” DNA, and it's very likely that there aren't any. Every other cell wasn't you, but became you... and those cells that have died or been lost have ceased to be you. FYI, I'll be going away for a couple of weeks, so it may be a bit before I can reply to any comments.