badvillain
Rookie
Nick Bostrom said:IIV. THE CORE OF THE SIMULATION ARGUMENT
The basic idea of this paper can be expressed roughly as follows: If there were a substantial chance that our civilization will ever get to the posthuman stage and run many ancestor-simulations, then how come you are not living in such a simulation?
We shall develop this idea into a rigorous argument. Let us introduce the following notation:
: Fraction of all human-level technological civilizations that survive to reach a posthuman stage
: Average number of ancestor-simulations run by a posthuman civilization
: Average number of individuals that have lived in a civilization before it reaches a posthuman stage
The actual fraction of all observers with human-type experiences that live in simulations is then
Writingfor the fraction of posthuman civilizations that are interested in running ancestor-simulations (or that contain at least some individuals who are interested in that and have sufficient resources to run a significant number of such simulations), andfor the average number of ancestor-simulations run by such interested civilizations, we have
and thus:
(*)
Because of the immense computing power of posthuman civilizations,is extremely large, as we saw in the previous section. By inspecting (*) we can then see that at least one of the following three propositions must be true:
(1)
(2)
(3)
V. A BLAND INDIFFERENCE PRINCIPLE
We can take a further step and conclude that conditional on the truth of (3), one’s credence in the hypothesis that one is in a simulation should be close to unity. More generally, if we knew that a fraction x of all observers with human-type experiences live in simulations, and we don’t have any information that indicate that our own particular experiences are any more or less likely than other human-type experiences to have been implemented in vivo rather than in machina, then our credence that we are in a simulation should equal x:
(#)
This step is sanctioned by a very weak indifference principle. Let us distinguish two cases. The first case, which is the easiest, is where all the minds in question are like your own in the sense that they are exactly qualitatively identical to yours: they have exactly the same information and the same experiences that you have. The second case is where the minds are “like” each other only in the loose sense of being the sort of minds that are typical of human creatures, but they are qualitatively distinct from one another and each has a distinct set of experiences. I maintain that even in the latter case, where the minds are qualitatively different, the simulation argument still works, provided that you have no information that bears on the question of which of the various minds are simulated and which are implemented biologically.
A detailed defense of a stronger principle, which implies the above stance for both cases as trivial special instances, has been given in the literature.[11] Space does not permit a recapitulation of that defense here, but we can bring out one of the underlying intuitions by bringing to our attention to an analogous situation of a more familiar kind. Suppose that x% of the population has a certain genetic sequenceS within the part of their DNA commonly designated as “junk DNA”. Suppose, further, that there are no manifestations of S (short of what would turn up in a gene assay) and that there are no known correlations between having S and any observable characteristic. Then, quite clearly, unless you have had your DNA sequenced, it is rational to assign a credence of x% to the hypothesis that you have S. And this is so quite irrespective of the fact that the people who have S have qualitatively different minds and experiences from the people who don’t haveS. (They are different simply because all humans have different experiences from one another, not because of any known link between S and what kind of experiences one has.)
The same reasoning holds if S is not the property of having a certain genetic sequence but instead the property of being in a simulation, assuming only that we have no information that enables us to predict any differences between the experiences of simulated minds and those of the original biological minds.
It should be stressed that the bland indifference principle expressed by (#) prescribes indifference only between hypotheses about which observer you are, when you have no information about which of these observers you are. It does not in general prescribe indifference between hypotheses when you lack specific information about which of the hypotheses is true. In contrast to Laplacean and other more ambitious principles of indifference, it is therefore immune to Bertrand’s paradox and similar predicaments that tend to plague indifference principles of unrestricted scope.
Readers familiar with the Doomsday argument[12] may worry that the bland principle of indifference invoked here is the same assumption that is responsible for getting the Doomsday argument off the ground, and that the counterintuitiveness of some of the implications of the latter incriminates or casts doubt on the validity of the former. This is not so. The Doomsday argument rests on a muchstronger and more controversial premiss, namely that one should reason as if one were a random sample from the set of all people who will ever have lived (past, present, and future) even though we know that we are living in the early twenty-first century rather than at some point in the distant past or the future. The bland indifference principle, by contrast, applies only to cases where we have no information about which group of people we belong to.
If betting odds provide some guidance to rational belief, it may also be worth to ponder that if everybody were to place a bet on whether they are in a simulation or not, then if people use the bland principle of indifference, and consequently place their money on being in a simulation if they know that that’s where almost all people are, then almost everyone will win their bets. If they bet on not being in a simulation, then almost everyone will lose. It seems better that the bland indifference principle be heeded.
Further, one can consider a sequence of possible situations in which an increasing fraction of all people live in simulations: 98%, 99%, 99.9%, 99.9999%, and so on. As one approaches the limiting case in which everybody is in a simulation (from which one can deductively infer that one is in a simulation oneself), it is plausible to require that the credence one assigns to being in a simulation gradually approach the limiting case of complete certainty in a matching manner.
[Source and citations: http://www.simulation-argument.com/simulation.html]
Last edited: