I've thought about this a lot in the context of the desire people seem to have to try and achieve human immortality or at least indefinite lifespans. If SciAm is correct here and the upper bound is a quadrillion bytes, we may not be able to hit that given the bound on possible human experiences, but someone who lived long enough would eventually hit that. After a hundred million years or whatever the real number is of life, you'd either lose the ability to form new memories or you'd have to overwrite old ones to do so.
Aside from having to eventually experience the death of all stars and light and the decay of most of the universe's baryonic matter and then face an eternity of darkness with nothing to touch, it's yet another reason I don't think immortality (as opposed to just a very long lifespan) is actually desirable.
I imagine there would be perhaps tech or technique which you can choose to determine which memories to compress and countless of others techniques like extra storage that you can instantly access, so I don't see all of these as being real arguments why not become immortal. If I have to choose to be dead and memoryless compared to losing some of my memories, but being still alive, why should I choose being dead and memoryless?
And when losing memories you would first just discard some details, like you lose now anyway, but you would start compressing centuries into rough ideas of what happened, it's just the details that would lack a bit.
I don't see it being a problem at all. And if really something happens with the Universe, sure I can die then, but why would I want to die before?
I want to know what happens, what gets discovered, what happens with humanity, how far do we reach in terms of understanding of what is going on in this place. Why are we here. Imagine dying and not even knowing why you were here.
My naive assumption would be that it would be a fairly gradual process. You'd just always have a sliding window of the last N years of memories, with the older ones being progressively more fuzzy and unreliable.
Aside from having to eventually experience the death of all stars and light and the decay of most of the universe's baryonic matter and then face an eternity of darkness with nothing to touch, it's yet another reason I don't think immortality (as opposed to just a very long lifespan) is actually desirable.