The question is important, as it’s often used as an argument against idea of immortality, on the level of desirability as well as feasibility. It may result in less interest in radical life extension as "result will be the same", we will die. Religion, on the other hand is not afraid to "sell" immortality, as it has God, who will solve all contradiction in immortality implementation. As a result, religion win on the market of ideas.
Immortality (by definition) is about not dying. The fact of eternal linear existence follows from it, seems to be very simple and obvious theorem:
“If I do not die in the time moment N and N+1, I will exist for any N”.
If we prove that immortality is impossible, then any life would look like: Now + unknown very long time + death. So, death is inevitable, and the only difference is the unknown time until it happens.
It is an unpleasant perspective, by the way.
So we have or “bad infinity”, or inevitable death. Both look unappealing. Both also look logically contradictory. "Infinite linear existence" requires infinite memory of observer, for example. "Death of observer" is also implies an idea of the ending of stream of experiences, which can't be proved empirically, and from logical point of view is unproved hypothesis.
But we can change our point of view if we abandon the idea of linear time.
Physics suggests that near black holes closed time-like curves could be possible. https://en.wikipedia.org/wiki/Closed_timelike_curve (Idea of "Eternal recurrence" of Nietzsche is an example of such circle immortality.)
If I am in such a curve, my experiences may recur after, say, one billion years. In this case, I am immortal but have finite time duration.
It may be not very good, but it is just a starting point in considerations that would help lead us away from the linear time model.
There may be other configurations in non-linear time. Another obvious one is the merging of different personal timelines.
Another is the circular attractor.
Another is a combination of attractors, merges and circular timelines, which may result in complex geometry.
Another is 2 (or many)- dimensional time, with another perpendicular time arrow. It results in a time topology. Time could also include singularities, in which one has an infinite number of experiences in finite time.
We could also add here idea of splitting time in quantum multiverse.
We could also add an idea that there is a possible path between any two observer-moment, and given that infinitely many such paths exist in splitting multiverse, any observer has non zero probability to become any other observer, which results in tangle of time-like curves in the space of all possible minds.
Timeless physics ideas also give us another view on idea of “time” in which we don’t have “infinite time”, but not because infinity is impossible, but because there is no such thing as time.
TL;DR: The idea of time is so complex that we can’t state that immortality results in eternal linear existence. These two ideas may be true or false independently.
Also I have a question to the readers: If you think that superintelligence will be created, do you think it will be immortal, and why?
The thing is, I'm just not sure if it's even a reasonable thing to talk about 'immortality' because I don't know what it means for one personal identity ('soul') to persist. I couldn't be sure if a computer simulated my mind it would be 'me', for example. Immortality will likely involve serious changes to the physical form our mind takes, and once you start talking about that you get into the realm of thought experiments like the idea that if you put someone under a general anaesthetic, take out one atom from their brain, then wake them up, you have a similar person but not the one who originally went under the anaesthetic. So from the perspective of the original person, undergoing their operation was pointless, because they are dead anyway. The person who wakes from the operation is someone else entirely.
I guess I'm just trying to say that immortality makes heaps of sense if we can somehow solve the question of personal identity, but if we can't, then 'immortality' may be pretty nonsensical to talk about, simply because if we cannot say what it takes for a single 'soul' to persist over time, the very concept of 'immortality' may be ill-defined.
I like your post about the heat death of the universe, if you ever figure anything out regarding the persistence of a personal identity, I'd like you to message me or something.
Isn't it purely a matter of definition? You can say that a version of you with one atom of yourself is you or that it isn't; or that a simulation of you either is or isn't you; but there's no objective right answer. It is worth nothing, though, that if you don't tell the different-by-one-atom version, or the simulated version, of the fact, they would probably never question being you.