[Paper] On the 'Simulation Argument' and Selective Scepticism

It seems as if your argument rests on the assertion that my access to facts about my physical condition is at least as good as my access to facts about the limitations of computation/simulation. You say the 'physical limitations', but I'm not sure why 'physical' in my universe is particularly relevant - what we care about is whether it's reasonable for there to be many simulations of someone like me over time or not.

I don't think this assertion is correct. I can make a statement about the limits of computation / simulation - i.e. that there is at least enough simulation power in the universe to simulate me and everything I am aware of, that is true whether I am in a simulation or in a top level universe, or even whether I believe in matter and physics at all.

I believe that this assertion, that the top level universe contains at least enough simulation power to simulate someone like myself and everything of which they are aware is something that I have better evidence for than the assertion that I have physical hands.

Have I misunderstood the argument, or do you disagree that I have better evidence for a minimum bound to simulation power than for any specific physical attribute?

It would be trivial for an SI to run a grainy simulation that was only computed out in greater detail when high-level variables of interest depended on it. Most sophisticated human simulations already try to work like this, e.g. particle filters for robotics or the Metropolis transport algorithm for ray-tracing works like this. No superintelligence would even be required, but in this case it is quite probable on priors as well, and if you were inside a superintelligent version you would never, ever notice the difference.

It's clear that we're not living in a set of physical laws designed for cheapest computation of intelligent beings, i.e., we are inside an apparent physics (real or simulated) that was chosen on other grounds than making intelligent beings cheap to simulate (if physics is real, then this follows immediately). But we could still, quite easily, be cheap simulations within a fixed choice of physics. E.g., the simulators grew up in a quantum relativistic universe, and now they're much more cheaply simulating other beings within an apparently quantum relativistic universe, using sophisticated approximations that change the level of detail when high-level variables depend on it (so you see the right results in particle accelerators) and use cached statistical outcomes for proteins folding instead of recomputing the underlying quantum potential energy surface every time, or even for whole cells when the cells are mostly behaving as a statistical aggregate, etc. This isn't a conspiracy theory, it's a mildly-more-sophisticated version of what sophisticated simulation algorithms try to do right now - expend computational power where it's most informative.

Another possibility is that whoever is running the simulation is both computationally very rich and not especially interested in humans, they're interested in the sub-atomic flux or something. We're just a side-effect.

The human brain is subject to glitches, such as petit mal, transient ischaemic attack, or misfiling a memory of a dream as a memory of something that really happened.

There is a lot of scope for a cheap simulation to produce glitches in the matrix without those glitches spoiling the results of the simulation. The inside people notice something off and just shrug. "I must have dreamt it" "I had a petit mal." "That wasn't the simulators taking me off line to edit a glitch out of my memory, that was just a TIA. I should get my blood pressure checked."

And the problem of "brain farts" gives the simulators a very cheap way for protecting the validity of the results simulation against people noticing glitches and derailing the simulation by going on a glitch hunt motivated by the theory that they might be living in a simulation. Simply hide the simulation hypothesis by editing Nick Bostrom under the guise of a TIA. In the simulation Nick wakes up with his coffee spilled and his head on the desk. Thinking up the simulation hypothesis "never happened". In all the myriad simulations, the simulation hypothesis is never discussed.

I'm not sure that entirely resolves the matter. How can the simulators be sure that editing out the simulation hypothesis works as smoothly as they expect? Perhaps they run a few simulations with it left in. If it triggers an in-simulation glitch hunt that compromises the validity of the simulation, they have their answer and can turn off the simulation.

The problem is more serious than that, in that not only is our universe computationally expensive, it is set up in a way such that it would (apparently) have a lot of trouble doing universe simulations. You cannot simulate n+1 arbitrary bits with just n qubits. This means that a simulation computer needs to be at least as effectively large as what it is simulating. You can assume that some aspects are more coarse grained (so you don't do a perfect simulation of most of Earth, just say the few kilometers near the surface that humans and other life are likely to be), but this is still a lot of stuff.

A fourth answer is that the entire world/universe isn't being simulated; only a small subset of it is. I believe that more arguments about simulations assume that more simulators wouldn't simulate the entire current population.

The other answer is that we are living in a much grainier simulation, and either there are super-intelligent demons flitting around between ticks of the world clock, falsifying the results of physics experiments and making smoke detectors work, or that there is a global conspiracy of some kind, orchestrated by the simulators, to which most of science is party, to convince the bulk of the population that we are living in a more computationally expensive universe.

To the extent that super-intelligent demons / global conspiracies are both required for a grainier simulation to work and unreasonable to include in a simulation hypothesis, this undermines your claim that "We could easily be supplied with a far, far grainier simulation and never know the difference. If you're interested in humans, you'd certainly take running many orders of magnitude more simulations, over running a single, imperceptibly more accurate simulation, far slower."

We live in something that is experimentally indistinguishable from an unbelievably computationally expensive universe... but there are whole disciplines of mathematics dedicated to discovering computationally easy ways to calculate results which are indistinguishable from unbelievably computationally expensive underlying mathematical models. If we can already do that, how much easier might it be for The Simulators?

Something doesn't click here. You claim "that we live in an unbelievably computationally expensive universe, and we really don't need to. We could easily be supplied with a far, far grainier simulation and never know the difference"; but how do we know that we do live in a computationally expensive universe if we can't recognize the difference between this and a less computationally expensive universe? Almost by definition anything we can measure (or perhaps more accurately have measured) is a necessary component of the simulation.

Thanks Benja. This is a good objection to the argument I make in the 'Rejecting Good Evidence' section of the paper, but I think I can avoid it by formulating BIP* more carefully.

Suppose I’m in a situation in which it currently appears to me as though f-sim = x. In effect, your suggestion is that, in this situation, my evidence can be characterized by the disjunction (A ∨ B). You then reason as follows:

(1) Conditional on A, my credence in SIM should be >= x.

(2) Conditional on B, my credence in SIM should be 1.

(3) So overall, given that A and B are mutually exclusive, my credence in SIM should be >= x.

I accept that this is a valid argument. The problem with it, in my view, is that (A ∨ B) is not a complete description of what my evidence says.

Let V represent the proposition that my evidence regarding f-sim is veridical (i.e., the true value of f-sim is indeed what it appears to be). If A is true, then V is also true. So a more complete description of what my evidence says is (A ∧ V) ∨ (B ∧ ~V).

Now we need to ask: is it true that, conditional on (A ∧ V), my credence in SIM should be >= x?

BIP doesn’t entail that it should be, since BIP takes no account of the relevance of V. And V is surely relevant, since (on the face of it, at least) V is far more likely to be true if I am not simulated (i.e., Cr (V | ~SIM) >> Cr (V | SIM)).

Indeed, if one were to learn that (A ∧ V) is true, one might well rationally assign credence =< x to SIM. However, it’s not important to my argument that one’s credence should be =< x: all that matters is that there is no compelling reason to think that it should be >= x.

In short, then, your argument shows that, conditional on a certain description of what my evidence indicates, my credence in SIM should be >= x. But that description is the not the most complete description available—and we must always use the most complete description available, because we often find in epistemology that incomplete descriptions of the evidence lead to incorrect inferences.

Nevertheless, I think your response does expose an error in the paper. I should have formulated BIP* like this, explicitly introducing V:

BIP*: Cr [SIM | ((f-sim = x) ∧ V) ∨ ((f-sim ≠ x) ∧ ~V)] >= x

When BIP* is formulated like this, it is not entailed by BIP. Yet this is the modified principle Bostrom actually needs, if he wants to recover his original conclusion while rejecting Good Evidence. So I think the overall argument still stands, once the error you point out is corrected.

(Updated)

I think your interpretation of "if I don't live in a simulation, then a fraction x of all humans lives in a simulation" as P(SIM or A) is wrong; it makes more sense to interpret it as P(A|¬SIM). This actually makes the proof simpler: for any A, B, we have that P(A) ≤ P(A|B)/P(B|A) by Bayes theorem, so if we accept that P(¬SIM|A) = (1-x), then we have P(¬SIM) ≤ (1-x)/P(A|¬SIM).

I've only skimmed the paper but AFAICT this wipes out its central claim. Good work.

Doesn't this argument trivially fail as a matter of logic, because assuming ~SH, we do in fact have good evidence about the expected future power of computation, so that if you accept the first two claims the third claim ~SH still becomes inconsistent as the original SA holds, hence SA still goes through?

Yes.

He's arguing against the version of SA where instead of SH being one of the options, "most people with experiences like ours are in simulations" is one of them. The section about rejecting "Good Evidence" deals with the version of SA where SH Is an option. He rejects it because the analog of the intuition pump used to justify the kind of anthropic reasoning used in the first version of SA isn't intuitive to him, but I think it's right.

is simply nonsensical to speak of entities in "another" universe simulating "our" universe, as the word universe already means "everything that exists."

This seems a silly linguistic nitpick - e.g perhaps other people use "universe" to mean our particular set of three dimensions of space and one dimension of time, or perhaps other people use "universe" to mean everything which is causally connected forwards and backwards to our own existence, etc.

If the Simulation Argument used the word "local set of galaxies" instead of "universe", would you still call it incoherent? If changing a single word is enough to change an argument from coherent to incoherent, then frankly you didn't find a fundamental flaw, you found a linguistic nitpick.