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I recently learned of the Simulation Argument, which attempts to show that one of three statements is very likely true, paraphrasing:

  1. Civilizations are unlikely to ever be able to simulate realities.
  2. Civilizations that are able to simulate realities will almost always choose not to do so.
  3. We're probably in a simulation already.

To arrive at (3), the argument goes: Suppose that civilizations do manage to simulate realities (with inhabitants) and those simulated inhabitants develop, then eventually those simulated inhabitants will make their own simulations, and on and on until there are many more simulations than there are "real" realities.

My question is:

Is the argument above compatible with the proposition that physical entities have finite information content?

The counterargument would go: Let N be the minimum number of bits required to describe all physical entities in R. (Such an N exists because physical entities have finite information content.) Then the total information content of all realities simulated within and/or nested beneath R, must be less than or equal to N, for if the total were greater than N then the simulation apparatus itself could not be contained in R. As a result, there cannot be an unlimited number (or even very many) simulated realities---Any given "real" reality could contain at most "about one" extra reality of comparable complexity, and then only if the simulation apparatus contained the bulk of the root reality's information content.

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    If we're in a simulation already, who's to say the simulators live in a reality remotely close to ours? If that's the case, then who is to say that any of the things we hold of this reality hold there? In short, once we allow (3) we seem to destroy our ability to say anything about this other reality, including how it can possibly relate to ours. A radically different reality we can't even envision decided to simulate this one with finite information. Seems we're at an impasse?
    – R. Barzell
    Commented Oct 9, 2015 at 23:53
  • @R.Barzell Good point, I suppose the finite information content proposition would need to be strengthened/clarified to be "Entities in all conceivable realities have finite information content," but that proposition is much harder to accept as an axiom than "Entities in realities (like ours) have finite information content."
    – Aaron Golden
    Commented Oct 9, 2015 at 23:57
  • Even then, is conceivability workable? Sure, some things seem impossible in all worlds (like square circles). However, is this due to our cognitive limitations, which may have been designed in us by the simulators? We can ground our reasoning in this universe by its effects and its analogies to other things, but once we step out of that, what do we have? Further, we can't just impose our rules as that's purely arbitrary and contradicts the transcendent nature of our premises. We need some rules within which to argue and some justification for those rules.
    – R. Barzell
    Commented Oct 10, 2015 at 0:35
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    Worth noting: the Simulation Argument makes an assumption of a perfect simulation, where nothing goes in or out of the simulation except the intended output. If simulations are imperfect, i.e. they have narrow pipes to allow reality to affect them and them to affect reality, there are many more options than just those the simulation argument posits.
    – Cort Ammon
    Commented Oct 10, 2015 at 5:41
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    I dunno. It seems to become meaningless either way, because either it matters for what we can know that we are in a simulator or it doesn't. If we go "thin" (i.e., say it doesn't), then the addition of simulations loses all meaning. If we go "thick" (i.e., say that since we are in a simulator, we cannot know what the outside reality is like at all), then it's also trivial. It would only work if there's some sort of middle. But I think you'll need to edit your question and spell out that middle. And my guess is that the stipulations re the thought experiment will spell out the answer.
    – virmaior
    Commented Oct 10, 2015 at 7:52

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No, it doesn't work to stop the argument, but it does introduce a pair of extra parameters which are the encoding efficiency e and the reality-simulation partition coefficient p. The latter measures what fraction of resources is devoted to "real" stuff vs. "simulated" stuff (1 = all real), while encoding efficiency measures how many simulated self-conscious philosophizing beings you can have per real being of that sort. These are both functions of layers of simulation, too; one might imagine that the outermost layer would have very inefficiently implemented "real" entities, and could compute existence much more inexpensively.

Now, if p << (1 - p) * e then the original argument still holds: there's just way more capacity devoted to simulated beings than real beings. And note that we couldn't tell because we don't know if we're on the outer layer or not.

So you just need an extra premise about the efficiency of the simulation to recover the original argument (flaws and all). In the absence of such a premise, the argument is incomplete; you can imagine a counterexample but unless you actually demonstrate it or take it as a premise, it doesn't "prove" the opposite.

(Quotes because the whole argument is a bit suspect because of dubious assumptions about the nature of simulations.)

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  • Thanks for the answer, these parameters clarify the situation for me. The problem in my thinking was the implicit assumption that there could not be, shall we say "super-conscious" simulators, capable of simulating self-conscious philosophizing beings at an encoding efficiency greater than one.
    – Aaron Golden
    Commented Oct 12, 2015 at 19:30

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