Stathis Papaioannou wrote:

Jesse Mazer wrote:

[Quoting Stathis:]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.

Jesse

If the rate of duplication of individuals always matches or surpasses the rate of destruction, then there will always be at least some individuals left. You can change "destruction" to "change beyond recognition" and the same argument applies. However, in a real world situation, all these paramaters will vary; most especially if we are talking about the decisions of sentient beings. In fact, even if the running average of these parameters were consistent over a sufficiently long time period (and I don't know that this is possible to guarantee: the average will vary over time, and the rate of change of the average will vary, and the second and third time derivative of the average will vary, and so on), given infinite time, there will be periods of negative overall growth which must result in extinction of any individual entity, or any group of entities, or the entire population.

You could be right, but I don't think you have good justification for being so confident that you're right. It seems plausible to me that the larger the number of copies that exist already, the smaller the variations in the doubling rate, the smaller the fluctuations in those derivatives you mention, and the smaller the probability that a temporary period of negative growth will continue for a given amount of time. Are you 100% certain this is wrong? Do you disagree that the average actions of a googolplex copies will probably be less uncertain than the average actions of 50 copies, for example?

You could be right, but I don't think you have good justification for being so confident that you're right. It seems plausible to me that the larger the number of copies that exist already, the smaller the variations in the doubling rate, the smaller the fluctuations in those derivatives you mention, and the smaller the probability that a temporary period of negative growth will continue for a given amount of time. Are you 100% certain this is wrong? Do you disagree that the average actions of a googolplex copies will probably be less uncertain than the average actions of 50 copies, for example?

It is analogous to the gambler's fallacy: given long enough, the gambler will lose everything, and then he won't have any funds to attempt to recover his losses.

If the odds are slightly in his favor on each individual bet (say, for each dollar he bets there is a 50% chance he'll lose it and a 50% chance he'll win $2.01), this isn't true; the larger the amount of money he has already, the more predictable his total winnings on each round of betting, so you could prove that there is some finite probability his money will never go to zero in an infinite number of rounds of betting.

If the odds are slightly in his favor on each individual bet (say, for each dollar he bets there is a 50% chance he'll lose it and a 50% chance he'll win $2.01), this isn't true; the larger the amount of money he has already, the more predictable his total winnings on each round of betting, so you could prove that there is some finite probability his money will never go to zero in an infinite number of rounds of betting.

This applies also to the casino, despite the odds being on average stacked in its favour: if it operates long enough, someone will break the bank. And in biology, even when a population is still well into the exponential phase of its growth, there is always the possibility that it will become extinct.

Yes, there is always the possibility, but as long as the resources for continued population growth exist, the probability of extinction in any given time interval should decrease the larger the population.

Yes, there is always the possibility, but as long as the resources for continued population growth exist, the probability of extinction in any given time interval should decrease the larger the population.

Jesse