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Alex_Altair comments on Computation Hazards - Less Wrong Discussion
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Many Worlds does not say that everything you can imagine exists in some universe. What does exist in some universe is determined by the Schrödinger equation, which is specific and limiting.
You are right. Many Worlds says that our universe exists in a superposition of many states, all of them governed by the same physical laws.
But if we assume the possibility of other universes with different physical laws (which I did implicitly), Solomonoff prior provides a framework for reasoning about them. Simply said, every universe exists, but some of them "exist more" and others "exist less", whatever that means. Simpler universes "exist more", complex universes "exist less"; each additional bit of description reduces the "existence" in half. Therefore very complicated universes have so little "existence" that we don't have to care about them.
This hypothesis feels even more weird than the Many Worlds hypothesis, but it explains some things that are otherwise difficult to explain, such as why our universe is fine-tuned for us. Without the hypothesis of multiple universes, the anthropic principle provides only a partial answer. It explains why we can't exist where we can't exist, but it does not explain why there is a universe where we can exist. On the other hand, if everything exists, why does our universe follow any laws? Solomonoff prior says that universes which follow laws "exist more", because it is easier to describe them (you only have to describe the initial state and the laws, not every possible exception). Thus, the anthropic principle + multiverse + Solomonoff prior together say that we do most probably exist in the simplest universe where we can exist; where simplest does not mean smallest in space and time, but most easy to fully describe mathematically. (Though I am not really sure if this universe really is simpler than other possible intelligent-life-containing universes. Maybe something is wrong with my explanation.)
I'm not sure about this, but I think if even some of the more complex universes run enumerative Turing simulations (basically, run every possible Turing machine, in order), one might expect most of our "real-ness" to come from complex universes simulating simple ones. Eliezer touches on this in Finale.
Are you saying that complex universes can run more simulations? Don't forget that complexity refers to Kolmogorov complexity, so simple universes can have tons of particles, but they all have the same properties. A complex universe would have just as many particles, but they would all have different physics. I'm not sure which of those universes is more capable of computation.
No, my point is that there are a lot of complex universes but the Kolmogorov ordering of Turing machines is universal, so universe complexity isn't transitive - a complex universe that starts a Kolmogorov search still runs the simple ones first.
That... is interesting.
Just out of curiosity, have you considered how this belief pays rent? I can see how it pays utils by letting us simulate people in this situation, but I wouldn't know how to determine whether it really paid utils.
The only way this belief is useful to me, is that it provides explanations to a few questions I would otherwise spend time answering; plus a wrong answer on them might make my real life worse.
First, avoiding generalized Pascal mugging: Yeah, everything is possible, including the chance that if I don't give you $1000 now, I will be tortured forever by an omnipotent sadist; but the probability is epsilon, so I won't give you those $1000 anyway.
Second, avoiding generalized quantum suicide: Yeah, whatever I do, in some universe it will have good consequences. And in some universe it will have bad consequences. But I should focus on whether the average (expected) results are positive or negative. For example, in case of a quantum suicide, the average result is me dead; in case of a lottery, the average result is not winning; in case of religion, the average result is no afterlife. On the other hand, when rationally doing useful things, the average result is more utilons.
The line between MWI and Tegmark Multiverse is not very clear, some of my arguments could be used for both. Using only MWI can answer questions about quantum randomness or generally about lawful randomness (which is probably on some level fueled by a quantum randomness: for example if I throw a coin, the exact movement of my muscles is determined by exact firing of my neurons, and a quantum event can make this signal a little bit weaker or stronger). But mere MWI cannot answer to questions like "what if this universe is just a simulation?", because that is outside of its framework (a simulation in what? possibly in a universe with different laws of physics? how do I calculate a probability of that?).