...assume that thelikelihood 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’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 1012harder, if we count the number of stars and black holes. According to the SA with linear scaling, being in simulation B is about 1012 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 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.
My view is that Kolmogorov is the right simplicity measure for probabilistically or brute force generated universes, as you also mention. But for intentionally generated universes the length and elegance of the program is not that relevant in determining how likely is a simulation to be run, while computational power and memory are hard constraints that the simulators must face.
For instance while I would expect unnecessary long programs to be unlikely to be run, if a long program L is 2x more efficient than a shorter program S, then I expect L to be more likely (many more simulators can afford L, cheaper to run in bulk, etc.).
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’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].
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 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.
My view is that Kolmogorov is the right simplicity measure for probabilistically or brute force generated universes, as you also mention. But for intentionally generated universes the length and elegance of the program is not that relevant in determining how likely is a simulation to be run, while computational power and memory are hard constraints that the simulators must face.
For instance while I would expect unnecessary long programs to be unlikely to be run, if a long program L is 2x more efficient than a shorter program S, then I expect L to be more likely (many more simulators can afford L, cheaper to run in bulk, etc.).