ARE YOU
LIVING IN A COMPUTER SIMULATION?
BY NICK BOSTROM
ABSTRACT
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 then these 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 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 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 ~1016-1017 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 ~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) 
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 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 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 much stronger 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.
VI.
INTERPRETATION
The
possibility represented by proposition (1) is fairly straightforward. If (1) is
true, then humankind will almost certainly fail to reach a posthuman level; for
virtually no species at our level of development become posthuman, and it is
hard to see any justification for thinking that our own species will be
especially privileged or protected from future disasters. Conditional on (1),
therefore, we must give a high credence to DOOM, the hypothesis that
humankind will go extinct before reaching a posthuman level:
One can imagine hypothetical
situations were we have such evidence as would trump knowledge of . 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 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 machine, and so
on, in arbitrarily many steps of iteration. If we do go on to create our own
ancestor-simulations, this would be strong evidence against (1) and (2), and we
would therefore have to 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, and the number could be increasing
over time. (One consideration that counts against the multi-level hypothesis is
that the computational cost for the basement-level simulators would be very
great. Simulating even a single posthuman civilization might be prohibitively
expensive. If so, then we should expect our simulation to be terminated when we
are about to become posthuman.)
Although all the elements of such a
system can be naturalistic, 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 inhabiting the
simulation: the posthumans created the world we see; they are of superior
intelligence; they are “omnipotent” in the sense that they can interfere in the
workings of our world even in ways that violate its physical laws; and they are
“omniscient” in the sense that they can monitor everything that happens.
However, all the demigods except those at the fundamental level of reality are
subject to sanctions by the more powerful gods living at lower levels.
Further rumination on these
themes could climax in a naturalistic theogony
that would study 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 dwellers of deeper levels. For example,
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 have a reason to behave ethically. The fact that it
has such a reason for moral behavior would of course add to everybody else’s
reason for behaving morally, and so on, in truly virtuous circle. One might get
a kind of universal ethical imperative, which it would be in everybody’s
self-interest to obey, as it were “from nowhere”.
In addition to
ancestor-simulations, one may also consider the possibility of more selective
simulations that include only a small group of humans or a 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.
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.
[Nick Bostrom's academic homepage: www.nickbostrom.com]
[More on the simulation argument: www.simulation-argument.com]