Are we but ghosts in the machine? pt. 3

So far in parts one and two of this series we have investigated the parts of Nick Bostrom’s Ancestor Simulation theory that suggest why and how a highly advanced civilization may create a fully-believable simulation of an entire world. Now let’s look at the chances that our world, the universe we experience every day, is in fact nothing more than such a simulation.

Better set some time aside for this, as we’re are going to invoke the darkest of all dark magic – scary maths.


So far we have discussed how it is impossible to determine for certain that a suitably advanced technological society would not have the desire or reason to create a simulation of an entire ancestral civilization (or any civilization for that matter – be it of the creators’ ancestors or a totally made-up civilization). We have also theorized that, even with the limitations of current technological development and the basic laws of physics as we understand them now it is not inconceivable that a system so advanced is possible that it would be able to replicate the human brain and functioning thereof, to the point of consciousness.

We have assumed that the creation of consious awareness in a system is not dependent on the physical structure of the brain or object in which the awareness grows and develops, as consciousness is a function of complexity rather that substrate.

We have also looked at the the idea of the “envatted brain” and concluded that, for all intents and purposes, providing that there is no frame of reference, there is pretty much no way for the simulant to know that he or she is such (the final part of the discussion will discuss in more detail the actual nuts and bolts of everyday life as a simulated being).

Let’s get mathematical

So, with all these assumptions in place, we can now look at the odds. What odds? Well, for fun, let’s look at the odds that human civilization is in fact so advanced that it has created such a simulation, and that the universe we know and love is in fact that very simulation. The idea that we are not in fact the modern humans – that we are in fact the ancestors, and simulated ones to boot. 

Now, this is a pretty far-fetched idea, right? That in the “real universe” it is not actually 2008, but some far-distant time (to us) when humans have mastered awesome computing power, perhaps using physics we can’t even comprehend yet (bearing in mind there is a lot of known physics we can’t comprehend now) and that for reasons unknown they have directed themselves to create a full simulation of life in 2008, from individual people to grass, to the sun, to the stars, insects, air, laws of physics and everything else. And that the simulants in there suspect nothing. Well, let’s see how it stacks up.

(Warning – the following will most likely only be fully understood by maths ninjas and people with enormous foreheads)

Bostrom illustrates the basic principle of his theory with some elegant mathematics. He applies it to a posthuman civilization (and uses the term) but in reality this can be seen as applied to any civilization, not necessarily human. Posthuman is just a convenient frame of reference.

He starts with three basic units:

 From this he ascertains that the actual fraction of observers living human-like experiences is therefore:

He then adds two extra elements:  to represent the number of posthuman civilizations able to run such a simulation as we have discussed (or at least with enough individuals who have the resources and interest to create such simulations), and  to represent the average number of Ancestor Simulations run by such a civilization. This gives us:

Which when added in would give us:

We have already discussed that the computing power of a posthuman civilization, in order to create such a simulation, would be immense, therefore  is a large value. If you follow the maths to its logical conclusion, by examining (*) it leaves you with three possibilities, one of which must be true:

Bland Indifference

Now, at this point, Bostrom discusses the Indiffrence Principle. Simply put, a strong Indifference Principle could be used against the outcome in (3) above to reduce the validity of the outcome, Basically, it suggests that by examining your experiences and realities you should be able to determine whether your existence is that of the real world or the simulation, and validate any theory as to which you are in from there. However, because the nature of such a simulation is that it is impossible to tell whether you are simulated or not, it cannot have any effect on the outcome or its validity.

To put it more simply, some would say “But, we know we are in the real world, because we breathe and because physics works as we predict and because I can feel the sun on my face, therefore (3) is invalid and the entire mathematical contruct is in error as we are in the real world, not the simulation.” Sadly, this argument does not hold any water as, if the sun on your face is merely a line of code telling your simulated mind that you are in the sunshine, or if the laws of physics as we know them work just fine because that is the way they are programmed to work, then you have no valid frame of reference and therefore no way to know which you are – real or simulated. In essence, a strong Indifference Principle requires that you know to which set you belong, but in a simulation this is impossible – meaning that it is also impossible to verify (3) as in error or not. He suggests that in place of a strong Indifference Principle, a weak or bland principle shoud be used, and actually validates (3). He explains:

“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:

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.”


 Pick a cup

So, now we have three conlusions, (1), (2) and (3), with the solution above giving unity to (3) – the possibility is that we are within an ancestral simulation of some kind. But let’s look at all three in more detail.


What is proposed by (1) is that the human race, or any other species on our planet,  will fail to reach a posthuman level of technological evloution which would allow it to create an ancestral simulation. Whilst it does not specifically say that we will all become extinct before reaching the posthuman stage, Bostrom asserts that there is:

“no 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.”

Basically, for (1) to be true, we’re all pretty much fucked.


With (2) the implication is less disastrous, but equally disheartening. For (2) to be true, it suggests that we are not within a simulation, but rather than this being so because of our own failings it is due to there being no desire to create such a simulation. For the number of Ancestor Simulations to be large, it corresponds that the number of creator posthuman civilizations will also be large.  For the number of simulations to be very low, or none, the number of posthuman civilizations may still be large, but there would have to be a convergence in that all these civilizations would have to consciously decide not to create such simulations.

This may be for a number of reasons. It is important to note that in all of human history there has been a strong desire to understand our past, and any historian given the resources to recreate an entire civilization – be it the Roman Empire, ancient Greece, World War Two or modern day society – anything – would jump at the chance. For (2) to be correct, it would suggest an inconceivable paradigm shift away from this natural curiosity – to know from where we came and how we ended up where we are – to one of indifference.

It’s not impossible, it should be supposed, that this may happen. Perhaps future posthuman society would have a very strong moral and ethical code that would see the creation of a simulation as causing unneccesary suffering to those within it. Such a civilization would be well aware that the entities within the simulation would be thinking, conscious beings, despite the fact they exist only in a computer program.  And creating a simulation without (simulated) pain, disease and suffering would render the simulation useless as the entire point of the excercise is to recreate true past events, not to create a shiny, peaceful utopia that never existed. Such a rainbow-colored program would serve no purpose and would offer no valid data.

Or, perhaps more simply, the posthuman society would be so far removed from us now that they would derive no benefit or value from such a simulation. Or maybe the things that bring us pleasure now – challenge, a desire for knowledge and an understanding of our past – would mean little to a future human society. It is possible that we cannot even comprehend the priorities of such a highly-evloved society.

Why would this be disheartening? It would be so because although it means that the human race survives long into the future and evloves beyond our wildest dreams, what happens here and now will be forgotten and never thought of – or be of any value – again. As a society we are a tribe of story tellers. We live through our history – stories of bravery, sacrifice, discovery, endeavor. As an example, consider survivors of World War One. There remain on this earth very few; most are long dead. But every year we comemmorate those who perished, and give thanks to those who did not. We celebrate the ultimate sacrifices and give thanks for the changes that resulted. Imagine if this was not the case – if such sacrifices were never even acknowledged and no-one now knew anything about it.  We are our history, we live it and breathe it, and without it we are very little. And to think that, no matter how much you strive to live on in memory once you are gone, you will ultimately be forgotten is a sad thought.


(3) is by far the most intriguing (and kinda scary) solution, and for this I will let Bostrom explain, as he does so much better than me:

“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.”

So, there you have it. In a nutshell, we either die out, are forgotten utterly, or don’t actually exist. And the scary maths suggest that of all these three, (3) is statistically the most likely.

In our final look at Ancestor Simulations, we’ll briefly touch on Bostrom’s view of what the greater implcations are for “life in a vat”, and what it would be like were we in one.




  1. Posted September 14, 2008 at 5:08 am | Permalink | Reply

    Wouldn’t our best way to reach posthuman be by not only learning how the simulation works but possibly finding a method to tranfer our program to the simulation above us to ensure our simulation is not destroyed. Become Gods of our own universe sort of speak

  2. Posted September 14, 2008 at 10:19 am | Permalink | Reply

    But there lies the difficulty – we would need to be aware that we are, in fact, simulated – and the likelihood of that I cover in part 4 🙂

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