ࡱ> 8:77 MbjbjUU "\7|7|Il~~~~~~~vvvv^2 $ v~ F ~~ F F F ~ ~ F F F ~~  p Gvp .0^,&F &F ~~~~Are You Living in a Simulation? February 7, 2001 Nick Bostrom [This is an early draft; please dont distribute] ABSTRACT Preliminaries Computationalism is a common assumption in the philosophy of mind. The idea is that mental phenomena arise when certain kinds of computations are performed, but it does not matter whether these computations are performed on carbon-based or silicon-based processors whether done in biological neural networks or in suitably detailed emulations of such networks on a computer. Arguments for this assumptions have been given in the literature [refs], and I will take it as a given here. At the current stage of technology, we dont have hardware that is powerful enough and software that is sophisticated enough to enable us to create conscious minds in computers. But persuasive arguments have been given that we avoid a species-destroying disaster and technological progress continues, then these technological limitations will eventually be overcome [refs]. Several authors argue that this stage may be only a few decades away, but for present purposes we dont have to make any assumptions about the time-scale. The argument I shall present works equally for those who think it will take hundreds of thousands of years to reach the posthuman stage of civilization, where humankind has acquired the technology that we already see is compatible with known physical laws [refs]. Such a mature stage of technological development will make possible the conversion of planets and other astronomical resources into enormously powerful computers. It is hard to currently be confident in any upper bound on the computing power that may be available to posthuman civilizations, because lacking a theory of everything we cant rule out the possibility of new physical phenomena not allowed for in current physical theories that may be utilized to transcend such limitations such as the Bekenstein bound [refs] that in our current understanding place a ceiling on the information processing density that can take place in a given lump of matter. But we can with much greater confidence establish lower bounds on posthuman computation, by assuming only mechanisms that are already known. For example, Eric Drexler [ref] estimates Anders Sandberg [ref] Robert Bradbury [ref] The amount of computing power needed to emulate a human mind can be roughly estimated Drexler [ref], Moravec [ref], Kurzweil [ref], Bostrom [ref] Simulating all sensory input a human brain receives in a lifetime requires If the environment is included in the simulation, this will require extra computing power. How much depends on the scope and granularity of the simulation. Simulating the entire universe down to the quantum level is obviously infeasible (unless radically new physics is discovered) but to get a realistic simulation of human experience much less is needed only what is required to ensure that the simulated humans, interacting in normal human ways with their simulated environment, dont notice any irregularities. The microscopic structure of the inside of the Earth can safely be left out. Distant astronomical objects can have highly compressed representations indeed: verisimilitude need extend only to the narrow band of properties that we can observe from our planet or solar system spacecraft. On the surface of Earth, macroscopic objects in inhabited areas may need to be continuously simulated. Microscopic phenomena could likely be filled in on an ad hoc basis. What you see when you look in an electron microscope needs to look unsuspicious, but you have usually have no way of confirming its coherence with unobserved parts of the microscopic world. Exceptions arise when we set up systems that are designed to harness unobserved microscopic phenomena operating according to known principles to get results that we are able to independently verify. The archetypal instance is computers. The simulation may therefore need to include a continuous representation of computers down to the level of individual logic elements. But this is no big problem, since our current computing power is negligible by posthuman standards. In general, the posthuman director would have enough computing power to keep track of the detailed belief-states in all human brains at all times. Thus, when it saw that a human were about to make an observation of the microscopic world, it could fill in sufficient detail in the simulation in the appropriate domain on an as-need basis. Should any error occur, the director could easily edit the states of any brains that have become aware of an anomaly before it spoils the simulation. Alternatively, the director can skip back a few seconds and rerun the simulation in a way that avoids the problem. It thus seems plausible that the main computational cost consists in simulating organic brains down to the neuronal or sub-neuronal level. As we build more and faster computers, the cost of simulating these may eventually come to dominate the cost of simulating nervous systems. Although its not possible to get a very exact estimate of the cost of a realistic simulation of human history, we use [] as a rough estimate. As we gain more experience with virtual reality, we will get a better grasp of the computational requirements for making such worlds appear realistic to their visitors. But in any case, even if our estimate is off by several orders of magnitude, this does not matter much for the argument we are pursuing here. We can conclude that the computing power available to posthuman civilizations is sufficient to run an very large number of ancestor-simulations even if they are devoting only a very minute fraction of their resources to that purpose we can conclude this even while leaving a huge margin of error in all our guesstimates. Posthuman civilizations would have enough computing power to hugely many ancestor-simulations even while using only a tiny minute fraction of their resources for that purpose. [Define ancestor-simulation; insert refs] The core argument The basic idea of the argument can be expressed roughly as follows: If transhumanists were right in thinking that we will 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: DOOM: Humanity goes extinct before reaching posthumanity. SIM: You are living in a simulation  EMBED Equation.3 : Average number of ancestor-simulations run by a posthuman civilization  EMBED Equation.3 : Average number of individuals that have lived in a civilization before it reaches a posthuman stage The fraction of all observers with human-type experiences that live in simulations is  EMBED Equation.3  Since the experiences an observer has if she is living in a simulation are indistinguishable from those she has if she is living in unmediated physical reality, it follows from a weak form of the principle of indifference that the probability of her living is a simulation equals the fraction of observers that live in simulation. Thus,  EMBED Equation.3  Writing  EMBED Equation.3 for the fraction of posthuman civilizations that are interested in running ancestor-simulations (or that contain at least some individuals with Jupiter-brain equivalent resources that are interested in that), and  EMBED Equation.3 for the average number of ancestor-simulations run by such interested civilizations, we have  EMBED Equation.3   EMBED Equation.3  (*) Because of the immense computing power of posthuman civilizations  EMBED Equation.3  is extremely large, as we saw in the previous section. By inspecting (*) we can see that at least one of the following three propositions must be true [insert proof in appendix] (1)  EMBED Equation.3  (2)  EMBED Equation.3  (3)  EMBED Equation.3  Interpretation The possibility represented by proposition (1) is fairly straightforward. There are many ways in which humanity could become extinct before reaching posthumanity. We are equating the probability of this happening with the fraction of all human-level civilizations that suffer this fate. Our estimates of these two quantities should be identical in the absence of evidence that our own civilization is special, by having either a lower or a greater extinction risk than other civilizations at our stage or development. One can imagine thought hypothetical situations were we did have such evidence for example, if we learn that we were about to be destroyed by a meteor impact. That might suggest that we had been exceptionally unlucky, so that we might regard our own probability of impending extinction as larger than the average for human-level civilizations. In the actual case, however, we seem to lack any ground for thinking us special. Proposition (1) doesnt by itself imply that we are likely to go extinct soon, only that we are unlikely to reach a posthuman stage. This possibility is compatible with us remaining at, or somewhat above, our current technological level of development for a long time before going extinct although this scenario does not fit within the transhumanist picture of the future. Another way for (1) to be true is if it is likely that technological civilization will collapse. Primitive human societies might then remain on Earth indefinitely. The most natural interpretation of (1) from a transhumanist perspective is that we are likely to go extinct as a result of the development of some powerful but dangerous technology. Molecular nanotechnology, which in its mature stage would enable the construction of self-replicating nanobots that can feed on dirt and organic matter, is a prime candidate. Such robots, designed for malicious ends, could cause the extinction of all life on the surface of our planet [refs]. This is sometimes known as the black goo scenario. The second alternative is that the fraction of posthuman civilizations that are interested in running ancestor-simulation is negligibly small. In order for (2) to be true, there has to be a fairly strong form of convergence among the courses of advanced civilizations [ref]. If the number of ancestor-simulations run by the interested civilizations is extremely large, the rarity of such civilizations must be correspondingly extreme. Virtually no posthuman civilizations decide to use their recourses to run large number of ancestor-simulations. Whats more, virtually all posthuman civilizations lack individuals with sufficient resources and interest to do that; or else they have reliably enforced laws that prevent their members from acting on their desires. What forces could bring about such convergence? One can speculate that advanced civilization all develop along a course that leads to the recognition of an ethical prohibition on running ancestor-simulation because of the suffering that causes for the inhabitants of the simulation. However, from our present point of view, it is not clear that creating a human race is immoral on the contrary, we tend to view the existence of our race as constituting a great ethical value. Moreover, convergence on an ethical view of the immorality of running ancestor-simulations is not enough: it must be combined with a convergence on a social structure that allows activities considered immoral to be effectively banned. (This might require convergence to a so-called singleton power structure among virtually all posthuman civilizations [ref].) Another possible convergence point is that almost all individual posthumans in virtually all posthuman civilizations develop in a direction were they lose their desires to run ancestor-simulations. This will require significant changes to the motivations driving their human predecessors, since there are certainly many humans who would like to run ancestor-simulations if they can afford it. But perhaps many of our human desires will be regarded as silly by any being that becomes a posthuman. Maybe the scientific value of ancestor-simulations to a posthuman civilization is negligible (which is not too implausible given it unfathomably superior intellectual sophistication), and maybe posthumans regard recreational activities as merely a very inefficient way of getting pleasure which can be obtained much more cheaply by direct stimulation of brains reward centers. One conclusion we can draw from (2) is that posthuman societies will be very different from human societies: they will not contain independent agents will human-like desires and who are free to act on them. The possibility expressed by alternative (3) is the conceptually most intriguing one. If we are living in a simulation, then the cosmos which we are observing is just a tiny piece of the totality of physical existence. The physics in the universe where the computer is situated which is running the simulation may or may not resemble the physics of the world we observe. While the world we see is in some sense real, it is not located at the fundamental level of reality. It may be possible for simulated civilizations to become posthuman. They may then run their own ancestor-simulations one powerful computers they build in their simulated universe. Such computers would be virtual machines, a familiar concept in computer science. (Java script web-applets, for instance, run on a virtual machine a simulated computer inside your desktop.) Virtual machines can be stacked: its possible to simulate a machine simulating another machine, and so on, for arbitrarily many iterations. If we do go on to create ancestor-simulations, then must conclude that we live in a simulation. Moreover, we would have to suspect that the posthumans running our simulation are themselves simulated beings; and their creators, in turn, may also be simulated beings. Reality may thus contain many levels. Even if it is necessary for the hierarchy to bottom out at some stage the metaphysical status of this claim is somewhat obscure there may be room for a large number of levels of reality to exist, and the number could be increasing over time. (One consideration that counts against the multi-level hypothesis is that the computational costs for the basement-level simulators would be very great. Simulating even a single posthuman civilization might be too expensive. If so, then we should expect our simulation to be terminated when we are about to reach the posthuman stage.) Although all the elements of such a world can be naturalistic, or even physical, it is possible to draw some loose analogies with religious conceptions of the world. In some ways, the posthumans running a simulation are like gods in relation to the people that inhabit them: the posthumans created the world we see; they are omnipotent in the sense that they can interfere in the workings of our world even in ways that violate its physical laws; they are omniscient in the sense that they can see everything that happens. However, all the demigods except those at the fundamental level of reality are subject to sanctions imposed upon them by the more powerful gods living on deeper levels. Further speculations may develop a systematic naturalistic theogony that studies the structure of this hierarchy, and the constraints imposed on its inhabitants by the possibility that their actions on their own level may affect the treatment they receive from inhabitants of deeper levels. [Note that if nobody can be sure that they are at the basement-level, then everybody would have to consider the possibility that their actions will be rewarded or punished, based perhaps on moral criteria, by their simulators. (An afterlife would be a real possibility.) Because of this fundamental uncertainty, even the basement civilization may choose to behave ethically. One might get a kind of universal ethical imperative, that it would be in everybodys self-interest to respect, as it were from nowhere.] Supposing we live in a simulation, what are the implications for us humans? Right now, the implications are relatively few. Our best guide to how our posthuman creators have chosen to set up our world is the standard empirical study of the universe we see. If, however, we learn more about posthuman motivations and resource constraints (maybe as a result of developing towards becoming posthumans ourselves) then the hypothesis that we are simulated may come to have a richer set of empirical implications. But for the moment, the effect on our belief system is very slight in proportion to our lack of confidence in our ability to understand the ways of posthumans). Properly understood, the truth of (3), although initially intellectually intriguing, should have no tendency to make us go crazy or to prevent us from going about our business. The main empirical importance of (3) at the current time is probably via its role in the tripartite disjunction that we established above. We may hope that (3) is true since it would decrease the probability of (1), although if computational constraints make it likely that simulators would terminate a simulation before it reached a posthuman level, then out best hope would be that (2) is true. This would entail a strong convergence hypothesis and practically no posthuman civilizations would contain wealthy individuals with human-like motives. Conclusion The conjunction of the denials of following three propositions is untenable: (1) The probability that humanity will go extinct before reaching a posthuman stage is very close to unity; (2) The fraction of posthuman civilizations that are interested in running ancestor-simulations is very close to zero; (3) The probability that we are living in a simulation is very close to unity. Given our ignorance, it seems reasonable to distribute ones doubt roughly evenly between the three conjuncts. We can conclude that one nave transhumanist dogma is false. The probability that you or your descendants will ever run an ancestor-simulation is negligible, unless you are now living in such a simulation. [Further topics:] [Various consequences of the assumption that you are in a simulation] [How this is different from the brain-in-a-vat problem] [chances vs. probabilities] [big cosmos] [relation to observational selection effects] [a note on infinities] [explain computationalism further] [the best-possible-world hypothesis; observer-moments] [on the physics of vast computations] [relation to explaining the apparent fine-tuning of our universe by the hypothesis that the physics at the basement-level isnt fine-tuned] mn  # $ % & 1 2 E F G H !!1!2!3!4!!!!~ j> EHUj*> CJUVaJ j` EHUjЎ*> CJUVaJ j6EHUj*> CJUVaJ jEHUjaX> CJUVaJ jEHUj*> CJUVaJ jEHUj*> CJUVaJ jU5\6]CJ", rs|}~r    GHlm^ & F`MKLM  ( ) !!!!!!"""#*#+#:#&)^ h^h ^!!!!!!!!!! " "" "!"""|"""""""""" # # # ###&#'#(#)#++??JKmKKM5\ jEHUj*> CJUVaJ jEHUj*> CJUVaJ jEHUjԓ*> CJUVaJ6] jEHUjX> CJUVaJ jbEHUjwX> CJUVaJ jU j1 EHUj*> CJUVaJ,)+.^15u7:<BHHIHTHKKKKK&KmKKKKKL6LmLLM  1h/ =!"#$%DdT/J   C A ? 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