A Bayesian Approach to the Simulation Argument
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mdpi.com
1) There is a fifty percent chance that the sort of word-simulations postulated by the simulation argument are not possible, and thus we live in reality not a simulation. 2) Even if such simulations are possible, there is a small but non-zero chance that we still happen to live in base reality.
By adding these two together, the paper concludes that we are slightly more likely to live in reality then a simulation.
The author attempts to justify the 50% assumption on the basis of the principle of indifference.
In situations where we really have no good idea of what the odds are, the principle of indifference seems to implicitly assume more knowledge than we actually have, allowing us to cloak our speculation in an aura of unjustified quantifiability.
Using a subjective Bayesian approach, in which Bayesian probabilities are just an expression of your own subjective judgement, you can choose priors on subjective personal grounds such as your intuition, whims, or desires (what you want to be true). By contrast, in objective Bayesianism, we need to provide some objective rational justification of the prior we choose, in which case it is hard to justify any initial prior for the simulation hypothesis than 0.5.
Does it really "implicitly assume more knowledge than we actually have"? To assign an epistemic probability of 0.5 exactly to a proposition is to be in a state of zero knowledge concerning its truth. As our knowledge moves away from zero, epistemic probability moves away from 0.5 and closer to either 0.0 or 1.0. To assign an epistemic probability of 0.5 exactly is to assume no knowledge at all.
This seems to me to be a slightly burden-shifting way to look at the issue. If one is assignining a more-or-less precise value - whatever it is - one should have a more-or-less solid reason for using that value and not some other.
> To assign an epistemic probability of 0.5 exactly is to assume no knowledge at all.
When, for example, I assign a probability of 0.5 to a fair coin showing heads after being tossed, I am most definitely not assuming no knowledge at all. If, on the other hand, I were asked to assume a probability for a scafwich showing a flantex after being zenquexed, I would have no basis for saying 0.5, or any other value.
Your example of tossing a fair coin is potentially confusing in that, for that specific example, both approaches to probability can produce the same answer, which can promote the confusion of treating them interchangeably.
If I have a coin which I don't know is fair, I can't assign a frequentist probability, but I can assign an objective Bayesian probability of 0.5, using either the principle of indifference or a uniform prior. Once I learn the coin is fair, I update the Bayesian probability, and it is still 0.5. Learning the fact that a coin is fair is not informative in terms of objective Bayesian probability, since it doesn't lead to any change in that probability. By contrast, learning that the coin is unfair is informative, and will lead to you updating to a different probability.
> If, on the other hand, I were asked to assume a probability for a scafwich showing a flantex after being zenquexed, I would have no basis for saying 0.5.
You have no basis to assign a frequentist probability. You do have a basis to assign an objective Bayesian probability of 0.5, the principle of indifference. And subjective Bayesian probabilities are subjective, so what subjective probability you assign is up to you.
First the flip way: how much are you prepared to bet on the outcome of one hundred trials in which a scafwich is zenquexed?
More seriously, as part of a process of Bayean updating, such as an experiment, the adoption of a starting position on the basis of the principle of indifference (or a uniform prior) is often a reasonable way to proceed, but in the case of both Bostrom's and Kipping's position on the simulation argument, no such process is performed, no empirical evidence is applied to the question, and the outcome is dominated by the prior, which, as you yourself seem to acknowledge, has no basis in current factual knowledge.
There is an important difference between, on the one hand, the ignorance of not being able to know in advance the outcome of a specific instance of a stochastic process, as in the case of a coin toss, and on the other hand, the ignorance of not knowing anything about the process itself.
> You do have a basis to assign an objective Bayesian probability of 0.5, the principle of indifference.
This seems to me to be begging the question.
> And subjective Bayesian probabilities are subjective, so what subjective probability you assign is up to you.
Exactly - neither me, you nor anyone else has any objective reason to believe this value to be more accurate than any other, and invoking the principle of indifference in these circumstances does not alter that fact.
It is not true that no empirical evidence is applied. To start with, future empirical evidence that arises in later historical periods could be very relevant – if a future observer observes running simulations, even nested simulations, that empirical evidence would greatly increase the probability of they themselves also being in a simulation, which would in turn raise the probability of us being in one now. If in the future we observed that technology being developed, but nobody being interested in using it, or a widespread moral prohibition being developed against it which is effectively enforced by the state – that would decrease its probability. If in the future we found ourselves in a state of seemingly terminal technological and economic decline, and our extinction seemed imminent, that would also decrease the probability. If after millions of years of future human technological development, we had still failed to develop this technology, that would support the idea that it is fundamentally infeasible, which in turn would reduce the probability the hypothesis is true.
It also isn't true that no contemporary physical evidence is relevant. If you read Bostrom's original paper, he cites results from physics (the Bremermann‐Bekenstein bound and the black hole limit) to support the idea that ancestor simulations may be feasible. Those results from physics are deduced from theories which are supported by empirical evidence (such as general relativity and quantum mechanics). If different observations had been made, supporting some other theories instead of establishing GR and QM, and from those theories we deduced something other than the Bremermann‐Bekenstein bound and the black hole limit, that might have led to a different conclusion about the physical limits of computation. If we exited in a universe in which the physical limits of computation were much lower, then the feasibility of ancestor simulations would be worse, and hence the simulation hypothesis would be less likely to be true.
> Exactly - neither me, you nor anyone else has any objective reason to believe this value to be more accurate than any other, and invoking the principle of indifference in these circumstances does not alter that fact.
There are two different ways of looking at "objective Bayesian probability": (1) as a school of thought, (2) as a claim about what epistemic probabilities we rationally ought to assign.
If we mean it as (1), then if you are calculating "objective Bayesian probability" according to the teachings of the adherents of that school of thought, then you have correctly calculated the "objective Bayesian probability". Whether you ultimately agree with the "principle of indifference", if that's what that school of thought teaches, it is part of "objective Bayesian probability".
If we are talking about sense (2), which I believe is the operative sense here – well, just as there is notorious disagreement about what is moral, or what morality requires – I would argue there is also heaps of disagreement about what is rational, or what rationality requires – it is just not as well-known (which is something I'd personally like to change).
So one person says "if we know nothing about the truth of hypothesis H, we should use the principle of indifference to assign it a prior probability of 0.5, and that is the epistemic probability we rationally ought to have with respect to it, until such time as we learn more". And you disagree, and say that's not what we rationally ought to do, at least not in this specific circumstance (although you appear to agree it may be what we rationally ought to do in other significantly different circumstances).
I'm not sure that difference in opinion about what is rational is fundamentally any easier to resolve than the notorious differences of opinion about what is moral (consider debates about the morality of abortion, the morality of the death penalty, sexual morality, etc)
That's a fair point about Bostrom's use of current knowledge, and his use of it in this case, to establish feasibility, is completely justified. I also have no doubts over justification in the case of arguments which say that current evidence raises or lowers the likelihood of something being so, and nor do I have doubts over justification in those cases where we say that if some proposition turned out to be true, then it would strengthen or weaken the case for a particular outcome. The only situation where I doubt the justification is where a specific numerical probability is assigned in a situation where we have no knowledge that argues for that particular value being most likely the correct one, and we are not in the process of (or about to start) an experiment or other investigation that will yield information to update that number, so that it is taken to be the final answer.
The principle of indifference seems to me to be a methodological assumption, rather than some sort of law: it gets the process of quantitative investigation started, but, like Occam's razor, it can be overruled by new information. One thing that would persuade me that the numbers yielded by applying the principle of indifference are objective is if there is a case where, if some different initial value were picked instead, Bayesean updating on the basis of relevant new, correct information would be incapable of converging on the actual value. I am fairly confident that there is no such case, and that Bayesean inference is robust against initial errors, when done with adequate correct information.
Perhaps one way to look at these two different responses to the simulation hypothesis is that we have started on an investigation, but are now waiting on empirical evidence, of the sort you mentioned in your first paragraph, that is not yet available. To me, it seems as if the specific numbers being used are "for illustrative purposes only" until we have some of that evidence. It may be that I am making an issue over something that everyone already understands.
A simple counter argument is that there's no reason the evil demon can't also coerce logic. For example, that we are in effect constantly entering into contradiction but are unable to see it by design.
Same applies here.
I'm certainly no expert on what Descartes meant precisely when he wrote that, but the broader point, that there is something that one can be sure of, certainly stands.
What exactly that something is might be hard to define. More recently it's been called "qualia", the thing that it's like to experience something.
"But some care is needed in using Descartes' argument. 'I think, therefore I am' says rather more than is strictly certain. It might seem as though we were quite sure of being the same person to-day as we were yesterday, and this is no doubt true in some sense. But the real Self is as hard to arrive at as the real table and does not seem to have that absolute, convincing certainty that belongs to particular experiences. When I look at my table and see a certain brown colour, what is quite certain at once is not 'I am seeing a brown colour', but rather, 'a brown colour is being seen'. This of course involves something (or somebody) which (or who) sees the brown colour; but it does not of itself involve that more or less permanent person whom we call 'I'. So far as immediate certainty goes, it might be that the something which sees the brown colour is quite momentary, and not the same as the something which has some different experience the next moment."
The question of whether or not when you see something, you see only the light or you see the thing you’re looking at, is one of those dopey philosophical things that an ordinary person has no difficulty with. Even the most profound philosopher, sitting eating his dinner, has many difficulties making out that what he looks at perhaps might only be the light from the steak, but it still implies the existence of the steak which he is able to lift by the fork to his mouth. The philosophers, who were unable to make that analysis, and that idea have fallen by the wayside from hunger.
Here is a full clip: https://themultidisciplinarian.com/2016/07/21/feynman-as-phi...
It’s similar to what David Hume, the great skepticist, observed centuries earlier, that one cannot really explain the endless “why” of physical processes, just the “how” of the apparent physical law determined by correlation.
Today we call it “shut up and calculate.”
We are only experiencing the end result of what our senses sample and our brain processes. That’s clearly true. How much that end result diverges from the real thing is difficult to answer, but in a straight forward way you can look at an optical illusion to see that there is some divergence.
Neither our sensory perception nor our language are entirely accurate representations of the world we live in, but they are both good enough for most purposes, so long as we don't get nerd-swiped into obsessing over questions of what it all means.
https://fs.blog/2012/01/richard-feynman-on-why-questions
A somewhat similar approach can be taken to the simulation question itself - rather than the default response of pondering the likelihood of it being true or how it might be implemented, I much prefer the ~"Is there any utility in the question itself?" approach taken by George Hotz starting at the 2:30 point in this interview on the Lex Fridman podcast:
https://www.youtube.com/watch?v=_SpptYg_0Rs
[Hotz] ...it wasn't a very practical talk about how to actually escape a simulation, it was more about a way of restructuring an us-versus-them narrative. If we continue on the path we're going with technology, I think we're in big trouble - like, as a species, and not just as a species but even me as an individual member of the species. So if we could change rhetoric to be more like...to think upwards...like, to think about that we're in a simulation and how we could get out...already we'd be on the right path. What you actually do once you do that, well, I assume I would have acquired way more intelligence in the process of doing that, so I'll just ask that.
[Fridman] So the the thinking upwards, what kind of ideas, what kind of breakthrough ideas do you think thinking in that way could inspire, and what did you say, upwards? Upwards into space are you thinking?
[Hotz] The space narrative that held for the modernist generation, doesn't hold as well for the postmodern generation. Like Elon Musk...like we're gonna build rockets, we're gonna go to Mars, we're gonna colonize the universe. The race to space. That was a great modernist narrative, but it doesn't seem to hold the same weight in today's culture. I'm hoping for good postmodern narratives that replace it.
My interpretation of his thinking is, regardless of whether we are actually in a simulation, it is possible to think of reality as a simulation - it (and the characters within it) behaves like a simulation, and it can be acted upon as one can act upon a simulation (changing variables, observing the result, etc)...so, let us (humanity) start to collectively conceptualize it in this manner, and collectively act upon it in a logical, coordinated, systemic manner. The benefit of this approach is it can help humanity and the individuals within it break out of this kind of "trance" we seem to be in where we kind of act and think as if the state of the world is mostly beyond our control, that ~"nothing can be done" beyond that what we are doing now (what we have ~always done).
Whether this idea would actually work is obviously speculative, but considering the existential predicament we find ourselves in, it seems to me like a fairly decent idea, especially compared to the competing ideas.
https://en.wikipedia.org/wiki/George_Hotz
The original talk being discussed in the interview:
Jailbreaking the Simulation with George Hotz | SXSW 2019
> Independent of his admitted naiveté and the job crisis in American physics, it is interesting to record how some leading physicists reacted to the physics he was doing. Clauser (2002a, p.71) reports that while he "was actually performing the first experimental test of the CHSH-Bell predictions as a postdoc at UC-Berkeley, [... he] made an appointment with Prof. Richard Feynman to discuss these same questions. Feynman was very impatient with [him]." Feynman's stance was: "Well, when you have found an error in quantum-theory's experimental predictions, come back then, and we can discuss your problem with it. " 82
> At this seminar, Aspect finished his talk by quoting a certain paper whose author derived results similar to Bell's inequalities and went on to discuss whether it was "a real problem." According to Aspect, this author gave an answer so unclear that he "had found it amusing to quote it as a kind of joke to conclude this presentation." Only at this point, did Aspect reveal the name of the author, Richard Feynman. According to Aspect, nobody in the audience laughed until Feynman laughed. Feynman checked the quotation and wrote to Aspect conceding he was right. 93
> [note 93]: [...] Feynman's quotation, in Feynman (1982, p. 471), is: "It has not yet become obvious to me that there's no real problem. I cannot define the real problem, therefore I suspect there's no real problem, but I'm not sure there's no real problem. So that's why I like to investigate things."
Still if such formulation is possible than the light that apparently reaches the philosopher from the food is an artifact of a model.
I remain pretty strongly agnostic about all this but I don't think you can escape it easily. One interesting thing to me would be what it would mean for some _rich_ far off signal to be picked up. It seems relatively easy for the universe to maintain a low fidelity simulation about rocks and radiation in space at a distance (plus or minus things like dark matter!) But if we suddenly started receiving broadcasts from an alien civilisation, or even met them face to face, that would be two very rich and detailed timelines that would suddenly have to snap into sync. That's certainly not something I'd allow if I had to build and maintain this stuff (and one can only assume unreasonable deadlines and budgets are universal).
And there's no reason why simulation requires everything to be simulated at the same time. Stars could be modeled as point masses, and only calculated in more detail when someone looks at them.
Take a look at the mandelbrot set https://math.hws.edu/eck/js/mandelbrot/MB.html infinite fractal complexity, shown using limited space + time.
[1]: https://www.drdobbs.com/jvm/an-algorithm-for-compressing-spa...
Even space complexity classes are not necessarily an issue. If the simulation runs out of storage, you can always suspend it, go provision more, and then resume it. The people in the simulation would never notice their suspension. It would only be a hard limit if some computation required more storage than could ever be provisioned, such as more bits than could fit in the observable universe. However, I doubt accurately simulating the contents of all contemporary human minds would need anywhere near that many bits.
In computer graphics terms. Culling. Objects are not simulated if u have no direct observer.
As Berkeley said, esse est percipi (to be is to be perceived)
That's one of the reasons why the simulation argument interests me. I think it may give one a reason to choose idealism over materialism. Idealism has a greater "simulation resistance" than materialism has. To a materialist, the question of whether we are living in a simulation may seem profound. An idealist can just shrug their shoulders.
A materialist has identified material reality as the most fundamental reality, and so the possibility that apparent material reality is not really the most fundamental reality does in some ways threaten the materialist worldview. For an idealist, for whom conscious minds and their experiences (qualia) are the most fundamental reality, the question of whether we are in a simulation is simply a question about whether their exist conscious minds who have the experience simulating us – and that may or may not be true, but either way it makes no difference to who or what we fundamentally are.
- By very definition, we will never be able to prove or disprove the claim.
- Whether or not it is the case, it makes no difference.
Why even bother? Why does this matter?
I don't think thats necessarily true. Here is a neat example: https://en.wikipedia.org/wiki/Weyl's_tile_argument
To simulate continuous space and/or time would be impossible, so if you could show that space/time is continuous then it could not be simulated.
Its interesting because the implications are interesting. Or rather, the implications of most other things are less interesting.
It's really unclear how you can turn "we live in a simulation" into a testable prediction.
If someone can make it scientific great! But Bostrom and Bayesian arguments are not doing science. It could be true, but we have no empirical reason to suspect so currently.
> Apart form (sic) 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.
Ecclesiastes 3:11 - He hath made every thing beautiful in his time: also he hath set the world in their heart, so that no man can find out the work that God maketh from the beginning to the end.
First, you have to consider all possible realities. We at least assume, if we're in a base reality, we're in one where at least one civilization developed after about 13 billion years or so and it has the ability to run computational simulations, though not even close to simulating a sentient animal brain. We can at least eliminate base realities where that never happens in trying to figure out which we're in.
What about past that? Assuming we're in base reality, how many futures result in becoming able to simulate sentient brains? How many possible presents contain other civilizations? How many time slices of our universe, if it is a base reality, contain more simulated observer moments than non-simulated?
How do you even begin to answer that? It isn't nearly as simple as Bostrom is making it seem. If some base reality civilization gains the ability to simulate but only has the computational capacity to try and trick Rick Sanchez into giving up the secret to making an interdimensional portal, that is several hours worth of one animal's observer moments versus however many some large number I don't know how to express worth of animal observer moments in base reality. There may need to be far, far more simulations than just "more than one" before the relative mass of simulated observer moments gets anywhere near the mass of real observer moments.
- in what broader execution context such a simulation could be managed, and
- whether the context of our simulation, itself, could have a meta-simulation above it.
The scientific inquiry is needful, but there just isn't any way we're going to know what happened before time0 outside of your metaphysical explanation of choice.
What exactly would actual, non - probabilistic evidence be? If we're in a VM x happens, if we're on bare metal y happens?