Jesse Mazer writes (after quoting Stathis Papaioannou):
No doubt, common implementations of your mind will predominate over more bizarre ones at any given point in time. It is also possible to imagine some scenarios where you survive indefinitely with all of your friends, for example implemented in an Omega Point computer. But eternity is a very long time. If it is possible that the Omega Point computer can break down, then, as Murphy teaches, it certainly *will* break down - eventually.
Not if the probability of it breaking down decreases in a geometric way from century to century (or millennium to millennium, aeon to aeon, whatever) as more and more of the universe is incorporated into the giant distributed computing network (or as the increasing computing power allows for more and more sophisticated ways of anticipating and avoiding civilization-ending disasters). Like I said, if the probability of a catastrophic breakdown was 1/8 in one century, 1/16 in the next, 1/32 in the next, and so on, then the total probability of it breaking down at any point in the entire infinite history of the universe would be the sum of the infinite series 1/8+1/16+1/32+1/64+1/128+... , which is equal to 1/4. In such a branch there'd be a 3/4 chance that civilization would last forever.
It is possible that the probability of the computer breaking down decreases geometrically with time, as you say. However, as t->infinity, it is nevertheless increasingly likely to deviate from this ideal behaviour, and the measure of branches of the multiverse in which it does will approach zero. Remember, it is not the probability in any single branch which is important (in fact, in the MWI that would be a meaningless concept), but the measure across all branches.
Also, you didn't address my other point, which is that even if all of civilization collapses around you, then if the probability of your continuing to survive would be even lower than the probability that the universe you have seen around you up until then is just part of a giant computer simulation in some branch where the technology exists to run such a simulation, then from your point of view you should expect it to be more likely that the beings running the simulation will decide to rescue you and bring you out into the "real world" than it is that you continue to survive alone at such incredibly long odds.
I'll have to think about this.
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