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?

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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 4 at 4:30
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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 4 at 7:11
  • 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 4 at 7:21
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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 4 at 11:04
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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 4 at 12:45

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.

  • @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 at 9:12
  • "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 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 at 4:35
  • 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 at 11:07
  • 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 at 8:21

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