On Falsifying the Simulation Hypothesis (or Embracing its Predictions)

Simpler simulations are more likely. But so are simpler universes. (For the same reason?)

To me it seems like "simulation" can refer to two different things:

• "passive simulation" where someone just sets up the rules and simulates the entire universe. This should be indistinguishable from a real universe that happened to have the same laws of physics.
• "active simulation" where someone intervenes in the universe, and causes miracles. Where miracles refer to anything that does not happen according to the internal laws of physics. It could be something seemingly non-magical, like inserting yourself in the universe as another seemingly ordinary human.

I guess we should be able to only detect the active simulation, by observing the miracles. Problem is, the miracles can be quite rare, and by definition we cannot replicate them experimentally.  If someone just magically entered this universe thousand years ago, had some fun but didn't do anything impactful (beyond the standard butterfly effect), and plans to return thousand years in the future... there is hardly an experiment we could set up to detect this. Heck, even if I told you "tomorrow at 12:00, somewhere on this planet a new adult human being will miraculously appear -- that's the avatar of the simulator", unless you happen to see this on camera, there is no way to prove it. There universe is complex enough so that you can't calculate how exactly the future should look like, therefore you will not notice a small change. (Unless the changes are intentionally made in the way that causes large change, e.g. if the simulator inserts themselves as a superhero who solves the greatest humanity's problems.)

An important consideration is whether you are trying to fool simulated creatures into believing simulation is real by hiding glitches, or you are doing an honest simulation and allow exploitation of these glitches. You should take it into account when you consider how deep you should simulate matter to make simulation plausible.

For example up until 1800-s you could coarse-grain atoms and molecules, and fool everyone about composition of stuff. The advances in chemistry and physics and widespread adoption of inventions relying on atomic theory made it progressively harder to identify scientists among simulated folks, so to be able to get to early 1900, your simulation should have grounding in XIX-th century physics, otherwise people in your simulation will be exposed to a lot of miracles.

In 1900-s it's quantum mechanics, Standard model, and solar system exploration (also, relativity but I don't know about complexity of GR simulation). I think you could still fool early experimenters into seeing double-slit experiments, convincingly simulate effects of atomic blasts using classical computers, and maybe even fake Moon landings.

But there are two near-future simulated events that will cause you to buy more computational power. The first one is Solar system exploration. This is less of a concern because in the worst case scenario, it's just an increase in N proportional to the number of simulated particles, or maybe you can do it more efficiently by simulating only visited surface - so not a big deal. 

The real trouble is universal quantum computers. These beasts are exponentially more powerful on some tasks (unless BPP=BQP of course), and if they become ubiquitous, to simulate the world reliably you have to use the real quantum computers.

Some other things to look out for:

• Is there more powerful fundamental complexity class at deeper than quantum level?
• Is there an evidence in nature of solving computational problems too fast to be reproduced on quantum computers (e.g. does any process give solutions to NP-hard problems in polynomial time)?
• Is there a pressure against expanding computational power required to simulate the universe?

Anthropic reasoning is hard.  It's especially hard when there's no outside position or evidence about the space of counterfactual possibilities (or really, any operational definition of "possible").  

I agree that we're equally likely to be in any simulation (or reality) that contains us.  But I don't think that's as useful as you seem to think.  We have no evidence of the number or variety of simulations that match our experience/memory.  I also like the simplicity assumption - Occam's razor continues to be useful.  But I'm not sure how to apply it - I very quickly run into the problem that "god is angry" is a much simpler explanation than a massive set of quantum interactions. 

Is is simpler for someone to just simulate this experience I'm having, or to simulate a universe that happens to contain me?  I really don't know.  I don't find https://en.wikipedia.org/wiki/Boltzmann_brain to be that compelling as a random occurrence, but I have to admit that as the result of an optimization/intentional process like a simulation, it's simpler than the explanation that there has actually existed or been simulated the full history of specific things which I remember.

...assume that the likelihood of a given simulation to be run is inversely correlated with the computational complexity of the simulation, in the space of all the simulation ever run. We can call the latter the Simplicity Assumption (SA)...

Isn't it possible that "simplicity" (according to one or more definitions thereof) need not care about the amount of raw computation required [0] to run any patch of simulation, nor with the volume of space it simulates? E.g. Occam's Razor [? · GW]'s measure of 'simplicity' (for AI) gives some function of the description length of a program running on a (universal) computer, so as to predict its own future percepts [1].

Now consider a civilization simulation A that is simulating in detail our solar system and mocking the rest of the universe and a simulation B which is simulating in detail the whole milky way and mocking the rest. Simulating in detail the milky way is about ${10}^{12}$harder, if we count the number of stars and black holes. According to the SA with linear scaling, being in simulation B is about ${10}^{12}$ less likely than being in A.

This particular example was what threw me off. In particular, we can presume that programs with shorter descriptions might better (i.e. more plausibly) simulate a complex system, and are more likely to be found by a computer/AI that iterates over possible programs, starting with the simplest one (like in Solomonoff Induction IIUC). This finds the shortest program that nonetheless sufficiently describes some observation sequence, which would not necessarily favor encoding special cases (i.e. "mocking") for costly things to simulate generally. Instead, mocking (since it optimizes for computational cost) might map to a different thing in Solomonoff, having the tradeoff of making the description more complex than the shortest possible one. 

For example, to simulate a human being acting within a nontrivial universe [2], one might hold that there must exist some mathematical structure that describes the human in all the ways we care about, in which case the runtime of their cognitive algorithms, etc. might have to be quite costly [3]. It might be more algorithmically probable, then, for such a human to be mapped to an algorithm built out of simple priors (e.g. laws of physics) instead of high-level code describing what the human does in various edge cases.

This isn't by any means a refutation of your argument, but rather just a thought provoker concerning the main premise of what the Simplicity Assumption should mean [4]. I agree with you and others that "simplicity" should be an organizing principle (that conditions one's priors over the types of possible universes). However, your post didn't coincide with my implicit definition of "simplicity". 

[0] (and possibly the amount of computation it seems to require)

[1] While your post isn't about AI generated universes, predictions made by an AI might well generate viable simulations (which might then become part of the hypothesis space under consideration). 

[2] Another prior holds that we don't appear to be privileged observers within our own universe; in a similar vein, neither might one (rationally?) hold that solipsism is a valid ontology over observers, etc..

[3] Admittedly, the example of accurately simulating one or more human doesn't rule out the possibility that only the observations that people notice are the ones that are simulated (per your view), the rest being "mocked." On this topic, I can only defer to AI related discussions like this [LW · GW] and here as to how one might begin to condition the probability space over types of (simulated) universes.  

[4] Though I don't personally know of a good argument in favor of the Speed Prior if we're talking about inductive inference leading to simulations.

I agree that simpler simulations are more probable. As a result the cheapest and one-observer-cenetered simulation are the most numerous. But cheapest simulation will have the highest probability of glitches. Thus the main observable property of  living in simulation is higher probability to observer miracles.

 Wrote about it here: "Simulation Typology and Termination Risks" and Glitch in the Matrix: Urban Legend or Evidence of the Simulation?

You mentioned at the end that as humanity does things that require a more complex simulation, such as exploring the rest of our solar system, the change of us being in a simple simulation (and therefore a simulation) reduce. How do you think this changes when you take into concideration the probabilities of us reaching those goals? A concrete example; our simulators might be running ancestor simulations to figure out "what is the probability of us discovering faster than light travel". To answer this they create 10^6 simple simulations of earth, with varying starting conditions. To answer their question they only need to simulate the solar system in significant resolution for those simulations who have explored it, which may be an slim slice of the overall set of simulations. In this example, a simulation who has explored the solar system cannot say "my simulation is computationally expensive to run, therefore there's a low chance of it being simulated" because the simulators can upgrade simple simulations to complex ones once they have reached sufficient complexity.

Have I got a point here? Many thanks for yours (or any onlookers) thoughts on the matter!

Appologies for the verbose phrasing of the question; "If you cannot explain it simply, you do not know it well enough" and I certainly don't know it well enough. :)

One caveat about the Simulation Hypothesis I haven't seen anyone commenting on: however advanced and capable of capturing/producing energy our simulators might be there should be some finite energy spent for each simulation. Assuming there are many concurrent simulations, minimizing the energy spent for each simulation seems to be an obvious objective for our simulators. One way is by sharing as much simulation data across simulations as possible and another would be by tweaking the simulated Physics to reduce how much of the Universe needs to be simulated (ie. supposing you are only interested in simulating Earth). Quantum MWI could be a hint of the former and The Holographic Principle could be a hint of the later.

I find it highly unlikely that we live in a simulation. Anyone who has implemented any kind of simulation has found out that they are hugely wasteful. It requires a huge amount of complexity to simulate even a tiny, low-complexity world. Therefore, all simulations will try to optimize as much as possible. However, we clearly don't live in a tiny, low-complexity, optimized world. Our everyday experiences could be implemented with a much, much lower-complexity world that doesn't have stuff like  relativity and quantum gravity and dark energy and muons.

The basic premise that simulations are basically the same as reality, and that there many simulations, but only one reality, and that statistically, we therefore almost certainly live in a simulation, is not consistent with my experience working on simulations. Any simulation anyone builds in the real world will by necessity be infinitely less complex than actual reality, and thus infinitely less likely to contain complex beings.