Jesse Mazer writes:
There are two separate probabilities to consider here. One is the probability (3/4, as you show) that civilization will never break down if implemented on a computer with behaviour as specified above. The other is the probability that the actual hardware will work according to specification. I don't think you should conflate the two, effectively arguing that the hardware will work to specification because that is part of the specification!
I don't think I ever said anything about the probability involving software only. If you have a distributed computing network (such that destroying any part of it won't cause a global breakdown), and more and more of the universe is constantly being gobbled up and converted into computing power, then perhaps the probability of all the hardware in the universe breaking down would decrease geometrically as well, on average. Assume that when I talk about the probability of all copies of you being destroyed decreasing like 1/8+1/16+1/32+..., this probability takes into account all possible causes of failure, including software problems, destruction of hardware, and even stuff like the possibility that some other enemy groups of A.I.'s will attempt to erase all copies of you.
Returning to the original question, once you have settled into your new home, what is to stop all your friends disappearing, as before? The computer will try to prevent this from happening, and you could probably try the geometric series trick again (i.e. decreasing probability that your friends disappear), but in this case there will be nothing tying you to those ever-rarer branches where the hardware works as it is supposed to.
But my point is that it doesn't necessarily have to be a matter of "ever-rarer" branches--even aside from quantum immortality, it might be true that in 3/4 (or whatever) of all branches stemming from a given point in time, any A.I. around at that time will have at least some copies around in the giant computing network forever.
You seem to be treating the proposed ever-decreasing failure rate per clock cycle as if it is something that will just happen inexorably once the denizens of the far future decide to build this computer.
No, I'm just suggesting that it's possible that once these far future people have gotten a good start on building this ever-increasing *network* of computers, the probability of every single computer in the system breaking down may, in an average world, be decreasing geometrically, perhaps for no other reason that the number of computers is increasing geometrically as more and more of the universe is converted into computing machines (which in a way would be no more surprising than the idea that the population tends to increase geometrically when resources are unlimited and death rates are low). This need not happen "inexorably" since it wouldn't be true in every single history, I'm just suggesting the average pattern if you look at all possible futures stemming from a given time may involve such a geometric decrease in failure probability. Are you suggesting it is somehow logically impossible that the *average* pattern would be a geometric one?
You may as well say that in the future, there will be computers with a mean time between failure of 10^10^100 years, or whatever arbitrarily large number you choose.
Sure, if you have a decentralized network of computers like the internet, then no matter what the average failure rate of an individual computer in the network, you can keep the failure rate of the entire network as arbitrarily low as you want by making the number of computers in the network sufficiently large.
The problem is not in conceiving of such super-machines, it is in the details of design and implementation.
Again, it need not be a question of super-machines, just a question of sheer numbers.
I imagine that in the future there may be multiple attempts to build computers which will squeeze an infinite period of subjective time into a finite period of real time, in the way you have described,
I wasn't necessarily suggesting an infinite number of computations in a finite physical time a la Tipler...an infinite number of computations in an infinite physical time a la Dyson would be fine too (to inhabitants of the simulation it wouldn't make any difference).
and like any other engineering project, the success rate will increase with increasing experience and resources, but even the "last gasp" effort in the moment before the big crunch will only succeed in an infinitesimally small proportion of multiverse branches.
I don't see why it is logically impossible that it could succeed in a non-infinitesimal proportion of multiverse branches, due to an on-average geometric decrease in the probability of the whole system breaking down.
You are relying on the availability of infinite resources for this ever-growing network
I would think that *any* scheme which proposed to allow civilization to do an infinite number of computations (whether in a finite physical time or an infinite physical time) would require infinite resources.
and disregarding such problems as the finite speed of communication,
Why am I disregarding that? I never suggested that all parts of the network would be able to communicate with each other quickly.
and the possibility that time is not infinitely divisible.
Again, this criticism would only apply to Tipler's scheme which proposes to pack an infinite number of computations into a finite physical time, it wouldn't apply to something like Dyson's scheme in an open universe whose expansion is decelerating. And given that we still don't have a theory of quantum gravity, it's possible there could be other ways of doing an infinite number of computations which don't match either scheme.
However, let us agree that the scenario you describe occurs in a non-negligible proportion of MW branches in which sentient life survives into the indefinite future, and return to Nick Prince's original question which spawned this thread. How will you ensure that your friends in this super-civilization running on this super-network will not disappear due to suicide, homicide, indefinite suspension or transformation into something completely unrecognizable? How will you ensure that *you* won't suicide, and end up in some other branch of the MW? If it possible that one of these things will happen, then over time, it will become a certainty, and you will be left alone. If there are constraints in place to make antisocial, self-destructive or simply perverse behaviour impossible, then (a) that would constitute more severe limits on freedom than the worst fascist state in our time, and (b) all fascist states fall, given time.
As I said earlier, my idea about seeing friends around is that A.I.'s in a giant computer network would periodically make copies of themselves, so even if a given copy commits suicide or is erased by accident or murder, there may be other copies in the network, and if the number of copies stemming from a single "common ancestor" (the number of copies belonging to a common 'clade') tends to increase geometrically, then the same logic about a finite total probability could apply here. Even so, with a friend you made fairly recently it may be that all copies descended from the common ancestor that you first met will end up getting erased, and of course none of the copies descended from earlier common ancestors would remember you, and they might be fairly different from the individual you knew. But if you have known someone for long enough that there are now a huge number of copies of the common ancestor you first met, spread throughout the network, then there might be a good chance that there'd be at least some copies descended from that common ancestor somewhere in the network until the end of time, no matter how many individual copies are erased.