Are You Living In A Computer Simulation?

ABSTRACT

This paper argues that at least one of the following propositions is true: (1) the human species is very likely to go extinct before reaching a “posthuman” stage; (2) any posthuman civilization is extremely unlikely to run a significant number of simulations of their evolutionary history (or variations thereof); (3) we are almost certainly living in a computer simulation. It follows that the belief that there is a significant chance that we will one day become posthumans who run ancestor-simulations is false, unless we are currently living in a simulation. A number of other consequences of this result are also discussed.

I. INTRODUCTION

Many works of science fiction as well as some forecasts by serious technologists and futurologists predict that enormous amounts of computing power will be available in the future. Let us suppose for a moment that these predictions are correct. One thing that later generations might do with their super-powerful computers is run detailed simulations of their forebears or of people like their forebears. Because their computers would be so powerful, they could run a great many such simulations. Suppose that these simulated people are conscious (as they would be if the simulations were sufficiently fine-grained and if a certain quite widely accepted position in the philosophy of mind is correct). Then it could be the case that the vast majority of minds like ours do not belong to the original race but rather to people simulated by the advanced descendants of an original race. It is then possible to argue that, if this were the case, we would be rational to think that we are likely among the simulated minds rather than among the original biological ones. Therefore, if we don’t think that we are currently living in a computer simulation, we are not entitled to believe that we will have descendants who will run lots of such simulations of their forebears. That is the basic idea. The rest of this paper will spell it out more carefully.

            Apart form the interest this thesis may hold for those who are engaged in futuristic speculation, there are also more purely theoretical rewards. The argument provides a stimulus for formulating some methodological and metaphysical questions, and it suggests naturalistic analogies to certain traditional religious conceptions, which some may find amusing or thought-provoking.

            The structure of the paper is as follows. First, we formulate an assumption that we need to import from the philosophy of mind in order to get the argument started. Second, we consider some empirical reasons for thinking that running vastly many simulations of human minds would be within the capability of a future civilization that has developed many of those technologies that can already be shown to be compatible with known physical laws and engineering constraints. This part is not philosophically necessary but it provides an incentive for paying attention to the rest. Then follows the core of the argument, which makes use of some simple probability theory, and a section providing support for a weak indifference principle that the argument employs. Lastly, we discuss some interpretations of the disjunction, mentioned in the abstract, that forms the conclusion of the simulation argument.

II. THE ASSUMPTION OF SUBSTRATE-INDEPENDENCE

A common assumption in the philosophy of mind is that of substrate-independence. The idea is that mental states can supervene on any of a broad class of physical substrates. Provided a system implements the right sort of computational structures and processes, it can be associated with conscious experiences. It is not an essential property of consciousness that it is implemented on carbon-based biological neural networks inside a cranium: silicon-based processors inside a computer could in principle do the trick as well.

Arguments for this thesis have been given in the literature, and although it is not entirely uncontroversial, we shall here take it as a given.

The argument we shall present does not, however, depend on any very strong version of functionalism or computationalism. For example, we need not assume that the thesis of substrate-independence is necessarily true (either analytically or metaphysically) – just that, in fact, a computer running a suitable program would be conscious. Moreover, we need not assume that in order to create a mind on a computer it would be sufficient to program it in such a way that it behaves like a human in all situations, including passing the Turing test etc. We need only the weaker assumption that it would suffice for the generation of subjective experiences that the computational processes of a human brain are structurally replicated in suitably fine-grained detail, such as on the level of individual synapses. This attenuated version of substrate-independence is quite widely accepted.

Neurotransmitters, nerve growth factors, and other chemicals that are smaller than a synapse clearly play a role in human cognition and learning. The substrate-independence thesis is not that the effects of these chemicals are small or irrelevant, but rather that they affect subjective experience only via their direct or indirect influence on computational activities. For example, if there can be no difference in subjective experience without there also being a difference in synaptic discharges, then the requisite detail of simulation is at the synaptic level (or higher).

III. THE TECHNOLOGICAL LIMITS OF COMPUTATION

At our current stage of technological development, we have neither sufficiently powerful hardware nor the requisite software to create conscious minds in computers. But persuasive arguments have been given to the effect that if technological progress continues unabated thenthese shortcomings will eventually be overcome. Some authors argue that this stage may be only a few decades away.[1] Yet present purposes require no assumptions about the time-scale. The simulation argument works equally well for those who think that it will take hundreds of thousands of years to reach a “posthuman” stage of civilization, where humankind has acquired most of the technological capabilities that one can currently show to be consistent with physical laws and with material and energy constraints.

Such a mature stage of technological development will make it possible to convert planets and other astronomical resources into enormously powerful computers. It is currently hard to be confident in any upper bound on the computing power that may be available to posthuman civilizations. As we are still lacking a “theory of everything”, we cannot rule out the possibility that novel physical phenomena, not allowed for in current physical theories, may be utilized to transcend those constraints[2] that in our current understanding impose theoretical limits on the information processing attainable in a given lump of matter. We can with much greater confidence establish lowerbounds on posthuman computation, by assuming only mechanisms that are already understood. For example, Eric Drexler has outlined a design for a system the size of a sugar cube (excluding cooling and power supply) that would perform 10²¹ instructions per second.[3]Another author gives a rough estimate of 10⁴² operations per second for a computer with a mass on order of a large planet.[4] (If we could create quantum computers, or learn to build computers out of nuclear matter or plasma, we could push closer to the theoretical limits. Seth Lloyd calculates an upper bound for a 1 kg computer of 5*10⁵⁰ logical operations per second carried out on ~10³¹ bits.[5] However, it suffices for our purposes to use the more conservative estimate that presupposes only currently known design-principles.)

The amount of computing power needed to emulate a human mind can likewise be roughly estimated. One estimate, based on how computationally expensive it is to replicate the functionality of a piece of nervous tissue that we have already understood and whose functionality has been replicated in silico, contrast enhancement in the retina, yields a figure of ~10¹⁴ operations per second for the entire human brain.[6] An alternative estimate, based the number of synapses in the brain and their firing frequency, gives a figure of ~10¹⁶-10¹⁷operations per second.[7] Conceivably, even more could be required if we want to simulate in detail the internal workings of synapses and dendritic trees. However, it is likely that the human central nervous system has a high degree of redundancy on the mircoscale to compensate for the unreliability and noisiness of its neuronal components. One would therefore expect a substantial efficiency gain when using more reliable and versatile non-biological processors.

Memory seems to be a no more stringent constraint than processing power.[8] Moreover, since the maximum human sensory bandwidth is ~10⁸ bits per second, simulating all sensory events incurs a negligible cost compared to simulating the cortical activity. We can therefore use the processing power required to simulate the central nervous system as an estimate of the total computational cost of simulating a human mind.

If the environment is included in the simulation, this will require additional 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 in order to get a realistic simulation of human experience, much less is needed – only whatever is required to ensure that the simulated humans, interacting in normal human ways with their simulated environment, don’t notice any irregularities. The microscopic structure of the inside of the Earth can be safely omitted. Distant astronomical objects can have highly compressed representations: verisimilitude need extend 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, but microscopic phenomena could likely be filled in ad hoc. What you see through an electron microscope needs to look unsuspicious, but you usually have no way of confirming its coherence with unobserved parts of the microscopic world. Exceptions arise when we deliberately design systems to harness unobserved microscopic phenomena that operate in accordance with known principles to get results that we are able to independently verify. The paradigmatic case of this is a computer. The simulation may therefore need to include a continuous representation of computers down to the level of individual logic elements. This presents no problem, since our current computing power is negligible by posthuman standards.

Moreover, a posthuman simulator would have enough computing power to keep track of the detailed belief-states in all human brains at all times. Therefore, when it saw that a human was 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-needed 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 could 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 in creating simulations that are indistinguishable from physical reality for human minds in the simulation resides in simulating organic brains down to the neuronal or sub-neuronal level.[9] While it is not possible to get a very exact estimate of the cost of a realistic simulation of human history, we can use ~10³³ - 10³⁶ operations as a rough estimate[10]. 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 our argument. We noted that a rough approximation of the computational power of a planetary-mass computer is 10⁴² operations per second, and that assumes only already known nanotechnological designs, which are probably far from optimal. A single such a computer could simulate the entire mental history of humankind (call this an ancestor-simulation) by using less than one millionth of its processing power for one second. A posthuman civilization may eventually build an astronomical number of such computers. We can conclude that the computing power available to a posthuman civilization is sufficient to run a huge number of ancestor-simulations even it allocates only a minute fraction of its resources to that purpose. We can draw this conclusion even while leaving a substantial margin of error in all our estimates.

·         Posthuman civilizations would have enough computing power to run hugely many ancestor-simulations even while using only a tiny fraction of their resources for that purpose.

IV. 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

Writing  for 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), and  for 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)        

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