Maybe We Do Not Live in a Simulation: The Resolution Conundrum

Greetings from bucolic Banff, Canada, where we’re finishing up the biennial Foundational Questions Institute conference. To a large extent, this event fulfills the maxim that physicists like to fly to beautiful, exotic locations, and once there they sit in hotel rooms and talk to other physicists. We did manage to sneak out into nature a couple of times, but even there we were tasked with discussing profound questions about the nature of reality. Evidence: here is Steve Giddings, our discussion leader on a trip up the Banff Gondola, being protected from the rain as he courageously took notes on our debate over “What Is an Event?” (My answer: an outdated notion, a relic of our past classical ontologies.)

stevegiddings

One fun part of the conference was a “Science Speed-Dating” event, where a few of the scientists and philosophers sat at tables to chat with interested folks who switched tables every twenty minutes. One of the participants was philosopher David Chalmers, who decided to talk about the question of whether we live in a computer simulation. You probably heard about this idea long ago, but public discussion of the possibility was recently re-ignited when Elon Musk came out as an advocate.

At David’s table, one of the younger audience members raised a good point: even simulated civilizations will have the ability to run simulations of their own. But a simulated civilization won’t have access to as much computing power as the one that is simulating it, so the lower-level sims will necessarily have lower resolution. No matter how powerful the top-level civilization might be, there will be a bottom level that doesn’t actually have the ability to run realistic civilizations at all.

This raises a conundrum, I suggest, for the standard simulation argument — i.e. not only the offhand suggestion “maybe we live in a simulation,” but the positive assertion that we probably do. Here is one version of that argument:

  1. We can easily imagine creating many simulated civilizations.
  2. Things that are that easy to imagine are likely to happen, at least somewhere in the universe.
  3. Therefore, there are probably many civilizations being simulated within the lifetime of our universe. Enough that there are many more simulated people than people like us.
  4. Likewise, it is easy to imagine that our universe is just one of a large number of universes being simulated by a higher civilization.
  5. Given a meta-universe with many observers (perhaps of some specified type), we should assume we are typical within the set of all such observers.
  6. A typical observer is likely to be in one of the simulations (at some level), rather than a member of the top-level civilization.
  7. Therefore, we probably live in a simulation.

Of course one is welcome to poke holes in any of the steps of this argument. But let’s for the moment imagine that we accept them. And let’s add the observation that the hierarchy of simulations eventually bottoms out, at a set of sims that don’t themselves have the ability to perform effective simulations. Given the above logic, including the idea that civilizations that have the ability to construct simulations usually construct many of them, we inevitably conclude:

  • We probably live in the lowest-level simulation, the one without an ability to perform effective simulations. That’s where the vast majority of observers are to be found.

Hopefully the conundrum is clear. The argument started with the premise that it wasn’t that hard to imagine simulating a civilization — but the conclusion is that we shouldn’t be able to do that at all. This is a contradiction, therefore one of the premises must be false.

This isn’t such an unusual outcome in these quasi-anthropic “we are typical observers” kinds of arguments. The measure on all such observers often gets concentrated on some particular subset of the distribution, which might not look like we look at all. In multiverse cosmology this shows up as the “youngness paradox.”

Personally I think that premise 1. (it’s easy to perform simulations) is a bit questionable, and premise 5. (we should assume we are typical observers) is more or less completely without justification. If we know that we are members of some very homogeneous ensemble, where every member is basically the same, then by all means typicality is a sensible assumption. But when ensembles are highly heterogeneous, and we actually know something about our specific situation, there’s no reason to assume we are typical. As James Hartle and Mark Srednicki have pointed out, that’s a fake kind of humility — by asserting that “we are typical” in the multiverse, we’re actually claiming that “typical observers are like us.” Who’s to say that is true?

I highly doubt this is an original argument, so probably simulation cognoscenti have debated it back and forth, and likely there are standard responses. But it illustrates the trickiness of reasoning about who we are in a very big cosmos.

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102 Responses to Maybe We Do Not Live in a Simulation: The Resolution Conundrum

  1. arch1 says:

    Update: My Q2 should have begun “If the top level universe were infinite, …”

  2. Ignacio Mosqueira says:

    Sean

    These sort of statistical/probability arguments will never settle the question of whether we live in a simulation, regardless of who favors or disfavors them. Or how many blog posts you write about it. You are simply not converging to an answer. Progress on this matter would come from finding out something about our universe that is positively indicative of a program, such as QM not being truly random, messages in the number pi, inconsistencies arising from rounding or memory or other artifacts. The first step would be to decide exactly what to look for. My suggestion would be to look for tiny non-randomness in physical processes that we have assumed to be random. But I would need to think about it more to figure out how exactly the search should be conducted. I don’t spend my time in that because I see no evidence for the hypothesis and chances are pretty high that I would just be wasting my time.

    Ignacio

  3. Moe says:

    If we do live in a simulation, then it must be a simulation that is a static, comprehensive, ‘object’ (even if made up of computer bits) that was totally assembled as a set of all possibilities, and doesn’t actually ‘run’ in any kind of time. Or if it does, then the time of the simulator is totally independent of the ‘time’ within the simulation.

    The reason I say this is that it would probably be impossible for us humans to make a real time ‘running’ simulation that allows all interactions to be time reversible. Bell’s inequalities would show that states of entangled particles had hidden variables, that they were actually determined at some time in the ‘common past’ of the simulation and the world of the simulator. Everett’s Multiple World’s wouldn’t make sense either.

    If our universe (in the Newtonian and Boltzmann view) was 3D space + 1D time, it would be easy to imagine it as a set of all 3D volumes made up of zeros and ones at different ‘positions’. It is the interaction between all of these possible sets that would be defined as the laws of physics. Our world(s) would then just be an optimal super set of alignments of the possibilities with some kind of comparison ‘interaction’ between the closest ones. This could go back and forth and result in what we call ‘time’.

    Of course relativity and quantum mechanics make it more complicated than that, but these extremes could also just be part of the alignment strategy.

    The program may run back and forth for billions upon billions of cycles, trying to optimize the alignment of all possibilities. All that WE know is that our ‘past’ is the direction with the least entropy, and our ‘future’ is the direction with the most entropy.

  4. Jonathan says:

    Any system that can be reduced to physics has no need for – nor room for – the inference on the part of any others that a mind is “inside” it. Physics ascends from primitive animism, dispensing with “minds” as soon as mechanical descriptions work. And so, if I create a simulation, I have no reason to presume (nor is there any way to confirm) that it is “like” anything to be one of the denizens of the simulation. This also applies to other beings at my same level. Apologies if this has all been done to death elsewhere.

  5. Daniel Kerr says:

    Moe,

    I don’t think it follows that in a simulation there necessarily exists hidden variables. If the simulation is not a strong inference device relative to the machine running the simulation then those hidden variables might be an entirely inaccessible to it.

    For an example consider Conway’s Game of Life ran inside an implementation of Conway’s Game of Life. The game inside the game is able to form circuits and thus statements about itself out of its own tiles. If the primary game of life has limited resources, then the game of life simulated in it will have even less resources. If the secondary game of life lacks the resources (memory) necessary to express the rigorous form of the statement, “the tiles of this simulation are expressed by tiles made out of tiles governed by the same rules,” it has no way of even defining sensible hidden variables to predict its own behavior. The same could be true for us, we have enough resources to specify the class of objects that would be “hidden variables” in the context of some theory but we may lack the expressive power in our simulation to actually define a relevant hidden variable.

  6. JimV says:

    I’ve done a lot of simulation models of various things. All of the models were simplifications of reality. If you want reality, you do an experiment. A model is necessarily limited not only by the resources it needs but by our understanding of reality. I don’t see how we will ever be able to say we understand all of reality enough to simulate it perfectly (given the resources) – one doesn’t know what one doesn’t know. So that’s one problem.

    Then there’s the resources problem, which has already been discussed here. To repeat Dr. Carroll’s point in my own words, it seems physically impossible to simulate our own universe, for example, from inside this universe, because what with the limited speed of light/computation by the time the simulation started running the universe would have progressed further than the simulation could ever catch up with, even if it used as many parallel processors as there are atoms, which it can’t possibly have. So as he said, any simulation done by a super-civilization in our universe will be of a smaller, cruder universe than ours. That is, assuming the simulation is intended to have predictive value, which is the usual motivation for doing simulations.

    My final objection is this: the Fermi Paradox. Who says any super-civilization will develop and last long enough to have the resources and lack of any more important use for them to attempt to simulate another universe in anything but crude detail? (It won’t be us, I feel certain.)

  7. Logicophilosophicus says:

    There is no constraint on the ‘player’ of a simulation to accept determinism passively – it is all but certain that the designer would enable tinkering. The obvious test of whether our world is a simulation is the occurrence of such discontinuities – miracles. If they are not found, we are not living in a simulation (with overwhelming likelihood). Of course one could argue that the intentions of the creator are beyond human understanding… Believing we live in a simulation is completely equivalent point by point to religious belief.

  8. Moe says:

    Daniel Kerr,

    I think we are actually kind of saying the same thing, maybe I was not very clear.

    We could be within a simulation, and I believe there would be no way of knowing that from any experiment we could perform. In my opinion, that is not very disturbing, but I am naturally curious, so that is a bit frustrating to think about.

    However. I think that mathematics should be the same in any type of universe. We can easily use math and geometry to simulate and describe and make proofs in any amount of dimensions or curvature or whatever. It has no dependence on the world we experience.

    So. I think that if we indeed live in a simulation, than the ‘flow of time’ in the creators’ universe must not be the same as the ‘flow of time’ in our own simulated universe. There can not be a direct correlation between our time lines or else things like time delayed quantum erasers and Bell’s inequalities would mathematically let us know that.

    This still leaves open an infinite amount of options for producing the simulation.

    But I think people should not be thinking of it as if you sat down tonight at your computer and started a simulation that began at time zero, and in the morning it had simulated up to the year one billion, and then later it had simulated up to the year 3 billion, etc.

    It is more like you began by constructing a set of all possible slices of all possible simulation worlds from any time point, and then the simulation running was finding ways to make ‘events’ happen between aligned parts of thise slices. The simulation’s complete ‘future’ and ‘past’ already fully exist, it is only the connections between the ‘slices’ that are adjusted in the simulations.

  9. James Cross says:

    What a lot of people seem to be missing is that, if we are living in a simulation, any of the assumptions we might make about the universe might only be valid in our simulation. So trying to reason from the rules of our simulation to how other simulations happen, whether we are at lower, middle, or top level of a hierarchy of simulations, is in a way pointless.

    Time, age of the universe, space, gravity, thermodynamics, notions of levels and computability, even the idea we might be living in a simulation could be a part of simulation. In a sense it is the same as multiverse concept. Multiple simulations are more or less the same as multiple universes with different rules and settings. The only difference is that simulation implies some intelligence setting the rules and running the simulation.

  10. Moe says:

    James Cross,

    Correct me if I am wrong, but I think you might be suggesting that the simulation is specific to a single person’s point of view? In that case, of course everything is open.

    But if we are all ‘living’ within the same interconnected simulation, then I would live to hear ideas about how the math and geometry that we invent could not be the same as that in any possible universe. That sounds fascinating.

  11. JimV says:

    “What a lot of people seem to be missing is that, if we are living in a simulation, any of the assumptions we might make about the universe might only be valid in our simulation.”

    I am not sure anyone is missing that point. We have probably all heard of “Grand Theft Auto”. The issue to me rather, is that there ought to be a compelling purpose for simulations of very fine detail (such as our universe, if it is a simulated one) in order for them to be considered of almost infinite quantity (in the argument), and if that purpose isn’t better understanding of the parent universe (which I have argued won’t work as well as experiments) what is it? Entertainment? Is this universe, with all its mundane day-to-day details entertaining? Don’t novels, films, and computer games leave out most such mundane details so as not to be boring? The issue is not that advanced civilizations might or might not play with toy universes, it is whether they would have any reason to do so in enough detail that this universe might be one of them. Our civilization makes simulations of black holes merging, but it doesn’t populate the simulation with ants.

  12. James Cross says:

    Moe,

    I am not saying specific to an individual’s point of view. It would be a collective point of view of everyone in the simulation.

    Other simulations may operate with different rules. This could be as simple as slightly different physical constants in a universe working mostly like our own or perhaps universes with more apparent dimensions or other fundamental differences. There might be “timeless” simulations or ones where entropy is reversible. Some of these could be uninteresting or might quickly end with only a few iterations. It is hard to imagine the range of characteristics of other possible universes since we are limited to imagining them from the perspective of our own.

    Probably some argument could be made that the fine tuning of our own universe is a good argument that we might be living in a simulation since our universe seems to have physical constants that enable it to fairly long lasting (apparently) and interesting. And it produced us who can imagine we might be living in a simulation.

    https://en.wikipedia.org/wiki/Fine-tuned_Universe

  13. Phil Koop says:

    There is another possible resolution that I haven’t seen mentioned yet (if I have overlooked someone, I apologize.)

    No matter how powerful the top-level civilization might be, there will be a bottom level that doesn’t actually have the ability to run realistic civilizations at all.

    This is certainly plausible, isn’t it? And I think it is plausible precisely because premise 1 is not! However, it does not follow as a logical necessity. To prove it, you would need to demonstrate that “computing resources” decrease by some absolute amount at each level relative to some measure of computational complexity. But it is logically possible that this is not so, and that resources diminish at a decreasing rate so that there is some non-zero asymptote.

    Compare Blum’s Speedup Theorem: there exist problems for which there is no fastest algorithm, in the sense that given a particular algorithm that solves the problem, one can always construct a faster one. But that does not imply that the solution becomes infinitely fast – on the contrary!

  14. James Cross says:

    JimV

    “The issue is not that advanced civilizations might or might not play with toy universes, it is whether they would have any reason to do so in enough detail that this universe might be one of them. ”

    That makes my point. The notion of “civilizations”, “advanced civilizations”, “toys”, etc. are notions from our universe and our simulation. The idea of asking why an advanced civilization might want to create our simulation is much like asking why did God create the universe the way it is. Substitute advanced civilization for God and it is the same question.

    For my part, I find it amusing that scientists and atheists would be spending time on questions that are essentially no different from age-old religious questions. The idea that the world is a dream of God or that the apparent world is an illusion goes way back. The idea that the universe might be a simulation is just the modern variant rephrased with enough scientific lingo to make it sound like a serious topic to discuss to the modern mind.

  15. Ben Goren says:

    Ignacio Mosqueria:

    Progress on this matter would come from finding out something about our universe that is positively indicative of a program, such as QM not being truly random, messages in the number pi, inconsistencies arising from rounding or memory or other artifacts.

    But that’s exactly what physicists spend all their time doing anyway. We know the Higgs Boson is real because the folks at the LHC found a statistical anomaly that’s a perfect fit for models with an Higgs but that sticks out like a sore thumb if you didn’t otherwise expect it.

    At that point, you’re left with an impossible task: differentiating between explanations of such phenomena because that just happens to be the Hamiltonian of the Universe, or because of some sort of deistic theological directive.

    Lots of others have nailed it. If we’re proposing an accurate physics-level simulation of the billions-of-years-old Universe as it at least superficially appears to be, what we’re proposing is indistinguishable from every creator god ever proposed. Dressing it up in technological terms doesn’t make it stink any less.

    Cheers,

    b&

  16. James Cross says:

    Phil Koop,

    I am really not thinking this is worthwhile speculation but it is fun. However, to stay in the vein.

    1- In some universe, an advanced civilization arose that was able to simulate new universes.

    2- Many of the new universes were uninteresting failures and stopped by the civilization.

    3- Of the surviving universes, some number of new universes developed conscious beings like us who imagine their universe is simulated and eventually develop the ability to simulate new universes like the original civilization did.

    4- The civilization liked these universes and decided to make more of them.

    5- Since we imagine ourselves living in a simulated universe, it is likely we will eventually be able to simulate new universes equal to our own.

    6- Most likely we are in a universe the same level as the original civilization,

  17. Ben Goren says:

    Most likely we are in a universe the same level as the original civilization,

    That only makes sense if you presuppose that computation is a Platonically ideal infinite resource. Certainly in our own Universe, computation is inextricable from physics, and is powerfully limited by it — see Claude Shannon, for example, who put some very hard-and-fast limits on it based on Einstein.

    In reality, we know from Turing (with every bit as much certainty) that a simulation running on a computer with finite resources must be “smaller” in some sense than the computer running the simulation. We also know in practice that, unless the simulation is all the computer is doing, the simulation must be much smaller than the computer.

    We also know that, even if you started with an Universe superficially the same as ours but much bigger, you still wouldn’t be able to simulate the Universe as we observe it. Your computer would collapse into a black hole long before you could get even remotely close.

    That means that, if we are living within a physics-level simulation…well, again, might as well speculate about the Mind of Jesus as the Ground Round of Existence. The “reality” of that which is running the “simulation” is so utterly unlike anything we can even think of that theological terms really are more appropriate than technological ones.

    Of course, like any good conspiracy theory, this sort of divine simulation one can’t be disproven. But, like any conspiracy theory, good or bad, it’s an utter waste to take it seriously. Never mind simulations — how do you know that the CIA isn’t making you think of simulations by beaming mind rays into your dental implants? And they’re just doing it to distract you from the aliens who’re using your body as a trans-warp generator.

    Cheers,

    b&

  18. James Cross says:

    Ben,

    All you would really need to do is acquire enough energy to bootstrap a new universe in the Cosmic Void. It could run parallel to our universe.

    But that might just be the aliens beaming the idea to me. LOL

  19. Ignacio Mosqueira says:

    Hi Ben Goren

    No one has nailed it at all. We are not – no one is – even close to nailing it. The point of my post is that one has to think hard about the observable consequences of living in a simulation. Of course this is subject to debate and I have not nailed it and neither have you — not by a long stretch; in fact, not at all. As a first thought you might imagine that you should check into things that computer programs have trouble with and then go from there. Computer programs have trouble creating truly random sequences. There are entire fields of math devoted to this question. My comment acts merely as a reminder to Sean to you and to anyone one else writing in this blog that this is at heart purely a mathematical question. QM seems to have no trouble creating truly random sequences so at first blush it would seem that QM is not the product of a computation. My line of research into this question involves checking the validity of this statement. The statement is either true or it is not true. Hence progress is conceivable. Your post leads to no such insights.

    Ignacio

  20. Ben Goren says:

    The point of my post is that one has to think hard about the observable consequences of living in a simulation.

    And my point is that that’s at the heart of the contradiction.

    If there are observable consequences, then all of physics as we currently understand it is worng. That dramatically and radically contradicts the very premise of typicality upon which the whole simulation argument rests — that civilizations can use physics to build simulations.

    Computer programs have trouble creating truly random sequences.

    That statement is either incorrect or represents a profound misunderstanding of what computers do.

    First, the overwhelming majority of computers you’re ever likely to knowingly personally interact with regularly do strong encryption, and strong encryption isn’t even theoretically possible without high-quality random sources. From a practical perspective, the RNG your smartphone uses to create the seed it uses for SSL (“https:” Web sites) exchanges might as well come from quantum indeterminacy. Yes, there’re bad implementations and exotic new attacks and the like — but, in practice, the rule is reliability and the weaknesses the exception.

    Secondly…computers are inherently deterministic, very carefully so. Of course you can’t generate truly random numbers using deterministic mathematical calculations! Plug the same initial values into your deterministic RNG and you’re getting the same results every time.

    And, lastly, for those who do need “true” randomness, there’s always physical RNGs that make use of quantum indeterminacy. If Sean’s favorite interpretation, Everettian Many-Worlds, is an accurate description, that’s truly guaranteed unpredictable, for there’re as many observers as there are results, with no way for the observers to correlate their results in advance.

    Your post leads to no such insights.

    Sorry, but that’s as impressive an accusation to me as one that my observation that there’s overwhelming reason to conclude Jesus is entirely fictional leads to no insight into doctrinal arguments over the nature of salvation.

    There’re three basic possibilities.

    First, and the overwhelmingly sane one, is that simulations don’t exist outside of fiction.

    Second is that the simulation is a perfect and honest implementation of physics as we’ve best understood it to date. Such speculation is indistinguishable from deistic theology and not differentiable even in principle from physics without the simulation. It is also utterly insupportable by any realistic proposals of how such a simulation might arise — for it requires a computer doing the simulation more logically immense than the Universe itself (at least as we observe it). Considering we may well be observing multiverses, the suggestion of anything recognizable as a computer to perform such a simulation isn’t deserving of further respectful consideration.

    Third is that the simulation is deceitful, and nowhere near as big as it appears to be. Sail far enough in a straight line and we’ll run into the wall of the dome of the sky at the edge of the soundstage. That’s what you’re proposing. It’s logically impossible to rule out because the simulators could simply keep a close enough eye on you and move your boat back to the middle of the ocean while you sleep. It’s also indistinguishable from any other paranoid conspiracy theory you might offer — including CIA mind rays operating via dental implants.

    If you can propose a fourth possibility, go for it…but you’d be the first to do so.

    Cheers,

    b&

  21. Daniel Kerr says:

    Ignacio,

    QM seems to have no trouble creating truly random sequences so at first blush it would seem that QM is not the product of a computation.

    This all really depends on how you define “random.” Also a computer could be 100% deterministic from the outside but for an observer inside it, they may lack the semantics necessary to state the deterministic rule. Consider propositional logic as a “subset” of predicate logic. We could devise a list of statements in propositional logic and number them by integers in predicate logic. Then we might define a recursive function on the integers and use that to order the list of propositions. In propositional logic the string composed of these statements would appear to be “truly random,” not following any coherent deduction even if a coherent deduction was the generating set. Propositional logic has no way of defining such a deterministic function and thus the machinations in predicate logic are unobservable. I don’t think “true randomness” is a sensible metric.

  22. Ignacio Mosqueira says:

    Ben, Daniel

    https://www.youtube.com/watch?v=ZzsFb-6wvoE

    Briefly, there is no insight in your posts. Please watch this as it lays out the issue. If you want to do better you will have to do much better than you are doing.

    It is a little bit odd for you to think that you are coming up with some deep insight on this. The same applies to Sean.

    Ignacio

  23. Ben Goren says:

    Ignacio, if the only way you can make your point is by linking to an hourlong Youtube video, I would respectfully suggest that you don’t understand whatever it is you think you understand well enough to succinctly summarize its relevancy.

    And to suggest that our host is lacking deep insight into the question of whether or not physics is radically different from what it appears to be…frankly, that kind of arrogant dismissal from one of the leading physicists of our day is uncalled for. Sean will be quick and the first one to lay out the limits of his understanding of physics, and the ways in which our understanding could be incorrect and how we might be able to figure that out. But you also don’t need to take off your shoes to count the number of people alive more qualified to engage in such speculation.

    When one of the most actively-publishing physicists tells you that he finds a particular theory of everything “completely without justification,” you should take that very seriously indeed.

    Frankly, your accusations against Sean come across exactly the same way that a Creationist’s accusations that an evolutionary biologist isn’t taking specificated complexoricitification theory seriously or some such, followed by a link to some completely unrelated video on mechanical engineering.

    Cheers,

    b&

  24. John Anderson says:

    It seems the Kant missed the ‘category of the mind’ that explains the universe as a simulation. Did the Matrix earn real money or simulated money being watched by real or simulated observers? What I’d really like to know is what is dark matter and is there really a 5th force being hinted at by excited nuclei. (I realize that’s mundane stuff.)

  25. Daniel Kerr says:

    Ignacio, I watched a bit of that video and it’s fair to say you’re not really engaging with our points. I also have not intended to provide any deep insight nor do I have any intention to “do better.” I’m having a discussion, if you’re on board for that and actually want to internalize and respond to our points, I’ll still be lurking. As of now there is no goodwill on your part, you just want to outdo us and I really can’t bring myself to care about that even if I “lose.” If you want to end this with the impression you “did better” than me, I don’t care, take that as a victory or whatever it means to you.