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OrphanWilde comments on Does immortality imply eternal existence in linear time? - Less Wrong Discussion
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Given that the human mind has a finite number of states, any given linear-immortal being, at some point in time, becomes indistinguishable from immortality with finite time duration.
I could become non human with arbitrary large mind size. But if we suggest that a finite upper limit of possible mind exist, like no more than 1 exobyte, then your objection works.
If we suggest that there is no upper limits of complexity of possible minds and AIs, then your objection doesn't work.
But some form of it may be still true. Because the larger the mind, the slower it works. Galaxy size mind would think one thought for 100 000 years. So it may result in some kind of limit of actual size of the minds, but more calculations are needed.