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ARE YOU LIVING IN A COMPUTER SIMULATION?
BY NICK BOSTROM
[Published in Philosophical Quarterly (2003) Vol. 53, No. 211, pp. 243 ‐255. (First version: 2001)]
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
theoretical limits on the information processing attainable in a given lump of
matter. We can with much greater confidence establish lower bounds 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 10
42 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*
50 logical operations per second carried
out on ~10 31 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 ~10 14 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 ~10 16 ‐ 1017
operations 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 ~10 8 bits per
second, simulating all sensory events incurs a negligible cost compared to
simulating the cortical activity. We can therefore use the processing power
of Information Processing Superobjects: The Daily Life among the Jupiter Brains.” Journal of
Evolution and Technology , vol. 5 (1999)).
(^3) K. E. Drexler, Nanosystems: Molecular Machinery, Manufacturing, and Computation , New York,
John Wiley & Sons, Inc., 1992.
(^4) R. J. Bradbury, “Matrioshka Brains.” Working manuscript (2002),
http://www.aeiveos.com/~bradbury/MatrioshkaBrains/MatrioshkaBrains.html.
(^5) S. Lloyd, “Ultimate physical limits to computation.” Nature 406 (31 August): 1047 ‐ 1054 (2000).
(^6) H. Moravec, Mind Children , Harvard University Press (1989).
(^7) Bostrom (1998), op. cit.
(^8) See references in foregoing footnotes.
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 ~
33 ‐ 10
36 operations as a
(^9) As we build more and faster computers, the cost of simulating our machines might eventually
come to dominate the cost of simulating nervous systems.
The actual fraction of all observers with human‐type experiences that live in
simulations is then
f NH H
f NH f
P
P sim
Writing f (^) I 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 N (^) I for the average number of ancestor‐simulations run
by such interested civilizations, we have
N fI N I
and thus:
P I I
P I I sim f f N
f f N f (*)
Because of the immense computing power of posthuman civilizations, N (^) I 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) fP 0
(2) fI 0
(3) fsim 1
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 :
Cr ( SIM | fsim x ) 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
sequence S 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
have S. (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
(^11) In e.g. N. Bostrom, “The Doomsday argument, Adam & Eve, UN++, and Quantum Joe.” Synthese
127(3): 359 ‐ 387 (2001); and most fully in my book Anthropic Bias: Observation Selection Effects in
Science and Philosophy , Routledge, New York, 2002.
must give a high credence to DOOM , the hypothesis that humankind will go
extinct before reaching a posthuman level:
Cr ( DOOM | fP 0 ) 1
One can imagine hypothetical situations were we have such evidence as
would trump knowledge of f (^) P. For example, if we discovered that we were
about to be hit by a giant meteor, this might suggest that we had been
exceptionally unlucky. We could then assign a credence to DOOM larger than
our expectation of the fraction of human‐level civilizations that fail to reach
posthumanity. In the actual case, however, we seem to lack evidence for thinking
that we are special in this regard, for better or worse.
Proposition (1) doesn’t 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 level of
technological development for a long time before going extinct. 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.
There are many ways in which humanity could become extinct before
reaching posthumanity. Perhaps the most natural interpretation of (1) is that we
are likely to go extinct as a result of the development of some powerful but
dangerous technology.
13 One candidate is molecular nanotechnology, which in
its mature stage would enable the construction of self‐replicating nanobots
capable of feeding on dirt and organic matter – a kind of mechanical bacteria.
Such nanobots, designed for malicious ends, could cause the extinction of all life
on our planet.
14
The second alternative in the simulation argument’s conclusion 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 must be a strong
convergence among the courses of advanced civilizations. If the number of
ancestor‐simulations created by the interested civilizations is extremely large, the
rarity of such civilizations must be correspondingly extreme. Virtually no
posthuman civilizations decide to use their resources to run large numbers of
ancestor‐simulations. Furthermore, virtually all posthuman civilizations lack
(^13) See my paper “Existential Risks: Analyzing Human Extinction Scenarios and Related Hazards.”
Journal of Evolution and Technology, vol. 9 (2001) for a survey and analysis of the present and
anticipated future threats to human survival.
(^14) See e.g. Drexler (1985) op cit., and R. A. Freitas Jr., “Some Limits to Global Ecophagy by
Biovorous Nanoreplicators, with Public Policy Recommendations.” Zyvex preprint April (2000),
http://www.foresight.org/NanoRev/Ecophagy.html.
individuals who have sufficient resources and interest to run ancestor‐
simulations; or else they have reliably enforced laws that prevent such
individuals from acting on their desires.
What force could bring about such convergence? One can speculate that
advanced civilizations all develop along a trajectory that leads to the recognition
of an ethical prohibition against running ancestor‐simulations because of the
suffering that is inflicted on 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
convergence on a civilization‐wide social structure that enables activities
considered immoral to be effectively banned.
Another possible convergence point is that almost all individual
posthumans in virtually all posthuman civilizations develop in a direction where
they lose their desires to run ancestor‐simulations. This would require significant
changes to the motivations driving their human predecessors, for there are
certainly many humans who would like to run ancestor‐simulations if they could
afford to do so. But perhaps many of our human desires will be regarded as silly
by anyone who becomes a posthuman. Maybe the scientific value of ancestor‐
simulations to a posthuman civilization is negligible (which is not too
implausible given its unfathomable intellectual superiority), 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 the brain’s reward centers. One conclusion that follows from (2) is
that posthuman societies will be very different from human societies: they will
not contain relatively wealthy independent agents who have the full gamut of
human‐like desires and 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 that we are
observing is just a tiny piece of the totality of physical existence. The physics in
the universe where the computer is situated that is running the simulation may
or may not resemble the physics of the world that 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 on 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: it’s possible to simulate a machine simulating another
single individual. The rest of humanity would then be zombies or “shadow‐
people” – humans simulated only at a level sufficient for the fully simulated
people not to notice anything suspicious. It is not clear how much cheaper
shadow‐people would be to simulate than real people. It is not even obvious that
it is possible for an entity to behave indistinguishably from a real human and yet
lack conscious experience. Even if there are such selective simulations, you
should not think that you are in one of them unless you think they are much
more numerous than complete simulations. There would have to be about 100
billion times as many “me‐simulations” (simulations of the life of only a single
mind) as there are ancestor‐simulations in order for most simulated persons to be
in me‐simulations.
There is also the possibility of simulators abridging certain parts of the
mental lives of simulated beings and giving them false memories of the sort of
experiences that they would typically have had during the omitted interval. If so,
one can consider the following (farfetched) solution to the problem of evil: that
there is no suffering in the world and all memories of suffering are illusions. Of
course, this hypothesis can be seriously entertained only at those times when you
are not currently suffering.
Supposing we live in a simulation, what are the implications for us
humans? The foregoing remarks notwithstanding, the implications are not all
that radical. 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. The
revisions to most parts of our belief networks would be rather slight and subtle –
in proportion to our lack of confidence in our ability to understand the ways of
posthumans. Properly understood, therefore, the truth of (3) should have no
tendency to make us “go crazy” or to prevent us from going about our business
and making plans and predictions for tomorrow. The chief empirical importance
of (3) at the current time seems to lie in its role in the tripartite conclusion
established above.
15 We may hope that (3) is true since that would decrease the
probability of (1), although if computational constraints make it likely that
simulators would terminate a simulation before it reaches a posthuman level,
then out best hope would be that (2) is true.
If 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 will come to have a much richer set of
empirical implications.
(^15) For some reflections by another author on the consequences of (3), which were sparked by a
privately circulated earlier version of this paper, see R. Hanson, “How to Live in a Simulation.”
Journal of Evolution and Technology , vol. 7 (2001).
VII. CONCLUSION
A technologically mature “posthuman” civilization would have enormous
computing power. Based on this empirical fact, the simulation argument shows
that at least one of the following propositions is true: (1) The fraction of human‐
level civilizations that reach a posthuman stage is very close to zero; (2) The
fraction of posthuman civilizations that are interested in running ancestor‐
simulations is very close to zero; (3) The fraction of all people with our kind of
experiences that are living in a simulation is very close to one.
If (1) is true, then we will almost certainly go extinct before reaching
posthumanity. If (2) is true, then there must be a strong convergence among the
courses of advanced civilizations so that virtually none contains any relatively
wealthy individuals who desire to run ancestor‐simulations and are free to do so.
If (3) is true, then we almost certainly live in a simulation. In the dark forest of
our current ignorance, it seems sensible to apportion one’s credence roughly
evenly between (1), (2), and (3).
Unless we are now living in a simulation, our descendants will almost
certainly never run an ancestor‐simulation.
Acknowledgements
I’m grateful to many people for comments, and especially to Amara Angelica,
Robert Bradbury, Milan Cirkovic, Robin Hanson, Hal Finney, Robert A. Freitas
Jr., John Leslie, Mitch Porter, Keith DeRose, Mike Treder, Mark Walker, Eliezer
Yudkowsky, and several anonymous referees.
www.nickbostrom.com www.simulation‐argument.com
