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Short version:

Has anyone tried arguing against Bostrom's argument's final postulate from the compressibility viewpoint?

Long version:

As per Nick Bostrom's simulation argument if people can make simulations and are interested in making them, then it is very likely that all of us are living in such simulations. So far I have not seen references of compressibility used as an argument against the final postulate of the argument "The fraction of all people with our kind of experiences that are living in a simulation is very close to one." In his talk with Lex Fridman he mentions that there is an assumption that the cost of such simulations is not comparable to the GDP of the simulators. However, I haven't found any basis of this assumption apart from the assumption that simulations can be run similar to how we run computer games at present.

If the simulations as the argument proposes are possible, then that inherently signifies that reality is compressible, because otherwise we would not be able to run a simulation at lower cost than running a real experiment. I believe that should be something we can test, if we can determine portions of our reality are compressible then we can say that either of the following 2 things is true:

  • The simulators are not running the optimum version of the simulation as further compression is possible. Or, atleast that we are not at the final level of simulation.
  • Our reality is real for all intents and purposes, as at best we could be an experiment run by an advanced species which wouldn't make us any less real.

If instead we find reality is incompressible (perhaps this can not be proven) then either of the following must be true:

  • The simulators are running the optimum version of simulation
  • No simulations (at least ones that run at lower cost than real experiments) are possible for us to run

Coming back to Bostrom's argument, if we do identify that our reality is compressible it would mean that fraction of people living in our level of simulation would not be close to one; that should be at least one level deeper of a simulation, because those simulations would be cheaper to run.

Has someone has used this line of reasoning against the simulation argument to date?

Rijul Gupta
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    Well, of course it is compressible. The laws of physics are basically a compression scheme for physical processes. If the universe wasn't compressible it would be completely incoherent and unpredictable. A stronger argument against simulationism is the concept of Boltzmann brains, which would vastly outnumber simulated brains. – causative Jan 04 '21 at 04:30
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    @causative: I did think about the physical laws, however the best of our simulations that work with physical laws deviate heavily from reality given enough time (which is often only a few hours or days). Even something as simple and macroscopic as newtonian laws aren't applicable to problems such as Newton's 3 body problem, because of the chaotic nature of the system and often we need to actually run the system to find answers instead of being able to use the laws to predict in advance. This hints at there not being a known way of reliably compressing reality as we know it. – Rijul Gupta Jan 04 '21 at 07:11
  • Having to actually run the system is a different concept from compression. Compression is only about the number of bits in the representation, not about how much computer time it takes to work with the representation. – causative Jan 04 '21 at 07:21
  • @causative I was thinking of compression temporally, but fair enough. Do you know of any work that has proven that the current state of known universe is compressible? I believe it might be fundamentally limited due to Heisenberg Uncertainty principle etc. – Rijul Gupta Jan 04 '21 at 07:26
  • Why lose your time countering the simulation argument at all ? All you need is 2 questions. 1 "how can you prove it is or is not the case ?", requiring not an abstract logical arguing it must be the case, but how, if our world is simulated, is it in any way different from a real world, how can we detect it. 2: what are you gonna do about it, how us your life gonna be any different than when you thought the world was real? Demand a factual, pragmatic answer, but expect none. – armand Jan 04 '21 at 10:43
  • @armand it seems that you are talking about the simulation hypothesis which is not equal to the simulation argument. The simulation argument tries to assign probabilities to different possibilities and seems slighlty more mathematically rigorous than the former. – Rijul Gupta Jan 04 '21 at 10:55
  • @RijulGupta It does not change a thing. If the simulated world is in no way distinguishable from a real one, and there is nothing to do about it but live our lives as if the world was real, who cares ? – armand Jan 04 '21 at 11:00
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    @armand I disagree, a lot of science and philosophy deals with understanding our position in this universe which doesn't change anything about how we live our lives. Some of these questions stem from our desire for deeper understanding of ourselves, why we have that yearning is not something I am personally interested in at the moment though. – Rijul Gupta Jan 04 '21 at 11:04
  • @RijulGupta: science change the way we live our lives by providing applicable knowledge. If you dont use it yourself, other people do put it in use and do change your life, even if you don't notice. Once you will have got yourself convinced either way about the simulation hypothesis, if it won't change your life in anyway you won't have gotten any knowledge about yourself. This is not philosophy. Please don't waste your time. – armand Jan 04 '21 at 11:48
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    @armand: I agree with almost everything you said. Do you have any reasons for assuming that finding out whether we are in a simulation or not has absolutely no way of changing your life in any meaningful way directly or indirectly? If not, let's leave it at that. – Rijul Gupta Jan 04 '21 at 12:45
  • it's in the comments above. It's the simulation hypothesis proponent's job to explain how his idea changes your life in any meaningful way. So far, i have met none who can answer the 2 questions. – armand Jan 04 '21 at 20:50
  • What if the number of bits required to precisely describe the observable universe is continually increasing, and so is the number of bits in all the computers in the observable universe? Then if you wanted to simulate the universe up to some time T1, there might always be some later time T2 at which intelligent beings would have the necessary memory and computing power needed to do so without compression. – Hypnosifl Feb 07 '21 at 18:12
  • @Hypnosifl I believe that reasoning may be flawed because that is assuming that at time T2 you can simulate a universe that requires b(T1) bits while itself existing with only b(T2)-b(T1) bits, which can not be greater than b(T1). – Rijul Gupta Feb 12 '21 at 09:06
  • @RijulGupta "b(T2) - b(T1)" would be something like the number of bits at T2 that were not devoted to performing the simulation of the universe at T1, yes? But I don't see why you say that can't be greater than b(T1), the equation b(T2) - b(T1) > b(T1) can be simplified by adding b(T1) to both sides of the inequality, giving b(T2) > 2b(T1). If the number of bits in the observable universe increases without bound, you could find a time T2 where the number of bits was more than twice as large as the number of bits at T1. – Hypnosifl Feb 12 '21 at 17:46
  • @Hypnosifl I made the classic error of stating something without mentioning my reasoning behind it. I think that if we do indeed have b(T2) - B(T1) > b(T1), then that implies that the bits in the universe are increasing without actually contributing anything to that particular universe, say they are some sort of "free" bits. – Rijul Gupta Feb 18 '21 at 04:31
  • When you say "without actually contributing anything to that particular universe", by "that particular universe" do you mean the real universe, not the simulated one? If I'm running a simulation on a computer, the physical elements storing the data about the simulated universe are still having all sorts of causal effects on the physical world outside of the computer (gravitational pull for ex.), so they are "contributing" to the outside universe in that sense. Also b(T2) could be much larger than 2b(T1) so the number of bits that aren't devoted to running simulations could be increasing. – Hypnosifl Feb 19 '21 at 00:51
  • @Hypnosifl I think I diverged from my original argument. If b(C) bits perfectly define a chicken, any chicken with b(C) bits will be real and not a simulation. If we make a chicken with b(C, T1) at T2, then that is a real chicken from time T1 and not a simulation. My original argument was that if b(C) can be compressed to b(C)' then we can run simulations (that have lower cost than running experiments); and if not, we are stuck with conducting real experiments suggesting either simulations are not possible at all or we are at the bottom of all the simulations. – Rijul Gupta Feb 19 '21 at 08:12
  • I just want to say I see this as a really fruitful direction. I've been thinking about whether a systems dynamics can be calculated in full, or not, in relation to what is real. Eg, dividing between *deterministic in principle* & *determinable*, as having different consequences, to whether a calculation can interact with our universe, & be considered 'real'. I don't have answers to your questions, but you might find this discussion interesting https://philosophy.stackexchange.com/questions/48769/are-we-living-in-a-simulation-the-evidence I see simulation arguments as great thought-experiments – CriglCragl Mar 10 '21 at 11:47

1 Answers1

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If the simulations as the argument proposes are possible, then that inherently signifies that reality is compressible, because otherwise we would not be able to run a simulation at lower cost than running a real experiment.

Here you are conflating the limitations and physics of our universe with the one of the simulators or of the sims. The simulators might have enough computational resources to he able to run the whole simulated universe in "realtime" if our physics is simpler. Or perhaps simply taking a lot of time to execute every frame of the simulation.

So the necessity of compressibility doesn't follow from the simulation argument.

Rexcirus
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  • @Rexcircus that would not be an exact simulation of reality as we experience it. My entire question is whether this level of reality is as simplified as it can be or not. If we can simplify the physics (and everything else) and still have an exact simulation of our current reality then that would prove that our reality is indeed compressible. – Rijul Gupta Feb 12 '21 at 09:12
  • "that would not be an exact simulation of reality as we experience it." Can you clarify? The simulators could run exactly our simulation, without any approximation, since their physics could be more complicated and powerful than the physics we experience, which for us is our reality, by definition. Or they could just live in a universe with the same physics, but vastly larger and with more resources. – Rexcirus Feb 12 '21 at 15:36
  • @Rexcircus: I was crtiquing your mention of running simulations with "simpler" physics. Let's say reality as we experience it can be completely defined with general relativity, and your simulator runs newtonian mechanics. While things might appear to work in this simulation, they would invariably deviate from the reality we experience because minor differences between general relativity and newtonian mechanics accumulating over scale. – Rijul Gupta Feb 18 '21 at 04:35
  • Got it, I just corrected that sentence to make it more clear. I was referring to the possibility of our physics being general relativity, while the simulators physics is perhaps Super gravity (or whatever physics that is more complicated than our universe physics) – Rexcirus Feb 18 '21 at 11:07
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    I think I am having a similar discussion with Hypnosifl in the comments on the question. My entire hypothesis/argument is that if you are using as many bits/computation/something as we already use to simulate reality, then it IS reality. Physics Engines (used in games) are real things we have made, but can a game simulate its own Physics Engine with less precision than is used to describe it? – Rijul Gupta Feb 19 '21 at 08:21
  • Have a look at Kolmogorov complexity, it may solve your doubts. By definition you cannot do better than that. – Rexcirus Feb 19 '21 at 13:45
  • well Kolmogorov complexity is a measure compressiblity and would define how much you can compress something if at all. I am not quite sure what you mean by not doing better than that. – Rijul Gupta Feb 19 '21 at 13:56
  • KC is the length of the shortest computer program that produces the object as output. So what you are really asking (if I understood) is if KC(object) < length_current_running_program_describing(object). Now use object = our universe for the simulation argument. The bad news is: KC is uncomputable. – Rexcirus Feb 19 '21 at 14:09
  • You are correct in that understanding, but KC might not be the best measure as it looks for an optimum, while merely finding an optima is enough to prove compressibility. Anyway, I am not asking about the computability of this at all, I am merely curious if someone has already tried to attack Nick Bostrom's Simulation Argument, or the general Simulation Hypothesis from this perspective. – Rijul Gupta Feb 19 '21 at 14:24
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    I'm working on something similar, but using computational resources instead of compressibility as main focus. Feel free to connect on linkedin (see my profile) I can send you a draft when it's ready. – Rexcirus Feb 19 '21 at 14:40
  • This is the point I always make in these arguments - under a simulation hypothesis, we cannot assume that we know anything about the world in which the simulators live other than probably basic logical / mathematical truths. Their physics could have any characteristics at all: maybe magic works and they used a spell to create the simulation - this no less probable than that their world is similar to ours. So we have no idea if 'compressibility' is a particularly useful notion - the pure maths bit of it may be applicable, but perhaps their computational resources have no relevant scarcity. – Rollo Burgess Nov 16 '21 at 17:36
  • Just to follow up, I published the article I was mentioning in the previous comment: https://lorenzopieri.com/sim_hypothesis/ – Rexcirus Nov 16 '21 at 17:57