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I'm no scientician, but wouldn't mutation mean that the possible number of gene combinations is constantly growing? And maybe even making previously non-viable permutations viable, which seems like it would really fuck with the math?
There would still be a limit as long as the species was constrained to modern homo sapien. Mutating yourself out of the species would mean you're no longer in the set of things.
I'm also no scientitian. I believe any mutations would have to be within the existing genome or else it would no longer be a biologically modern human.
Let's add the additional stipulation that we are not adding any meaningless genes. I know that there are a lot of them, but I'm just curious about what the math would look like and if we even have the knowledge about the genome to know which gene variations are meaningful.
I'm thinking of the doppelganger thought that experiment. Am I really the only person like me that has ever lived or what level or live? Or is it statistically possible that another genetically identical version of me could exist within the timeline of the universe (as I mentioned, with a 50% probability or better)?