`Hal Finney wrote:`

I think the problem with your argument is that you are assuming that all physical arrangements of matter appended to the universe are equally likely. And in that case, you are right that some random arrangement would be far more likely than one which looks like an observer who has set up a computer to simulate our universe.

However, I prefer a model in which what we consider equally likely is not patterns of matter, but the laws of physics and initial conditions which generate a given universe. In this model, universes with simple laws are far more likely than universes with complex ones.

Why? If you consider each possible distinct Turing machine program to be equally likely, then as I said before, for any finite complexity bound there will be only a finite number of programs with less complexity than that, and an infinite number with greater complexity, so if each program had equal measure we should expect the laws of nature are always more complex than any possible finite rule we can think of. If you believe in putting a measure on "universes" in the first place (instead of a measure on first-person experiences, which I prefer), then for your idea to work the measure would need to be biased towards smaller program/rules, like the "universal prior" or the "speed prior" that have been discussed on this list by Juergen Schimdhuber and Russell Standish (I think you were around for these discussions, but if not see http://www.idsia.ch/~juergen/computeruniverse.html and http://parallel.hpc.unsw.edu.au/rks/docs/occam/occam.html for more details)

Why? If you consider each possible distinct Turing machine program to be equally likely, then as I said before, for any finite complexity bound there will be only a finite number of programs with less complexity than that, and an infinite number with greater complexity, so if each program had equal measure we should expect the laws of nature are always more complex than any possible finite rule we can think of. If you believe in putting a measure on "universes" in the first place (instead of a measure on first-person experiences, which I prefer), then for your idea to work the measure would need to be biased towards smaller program/rules, like the "universal prior" or the "speed prior" that have been discussed on this list by Juergen Schimdhuber and Russell Standish (I think you were around for these discussions, but if not see http://www.idsia.ch/~juergen/computeruniverse.html and http://parallel.hpc.unsw.edu.au/rks/docs/occam/occam.html for more details)

Therefore I'd suggest that when you consider the possibility that our universe is embedded in a larger structure, you can't just look at the matter complexity of that structure. Rather, you should look at the physical-law complexity. And it seems plausible to me that the physical laws of the outer universe don't necessarily have to be much more complex than our own. In fact, it may be that we are capable of simulating our own universe (we don't know the laws of physics well enough to answer that question, IMO).

If the "everything that can exist does exist" idea is true, then every possible universe is in a sense both an "outer universe" (an independent Platonic object) and an "inner universe" (a simulation in some other logically possible universe). If you want a measure on universes, it's possible that universes which have lots of simulated copies running in high-measure universes will themselves tend to have higher measure, perhaps you could bootstrap the global measure this way...but this would require an answer to the question I keep mentioning from the Chalmers paper, namely deciding what it means for one simulation to "contain" another. Without an answer to this, we can't really say that a computer running a simulation of a universe with particular laws and initial conditions is contributing more to the measure of that possible universe than the random motions of molecules in a rock are contributing to its measure, since both can be seen as isomorphic to the events of that universe with the right mapping.

If the "everything that can exist does exist" idea is true, then every possible universe is in a sense both an "outer universe" (an independent Platonic object) and an "inner universe" (a simulation in some other logically possible universe). If you want a measure on universes, it's possible that universes which have lots of simulated copies running in high-measure universes will themselves tend to have higher measure, perhaps you could bootstrap the global measure this way...but this would require an answer to the question I keep mentioning from the Chalmers paper, namely deciding what it means for one simulation to "contain" another. Without an answer to this, we can't really say that a computer running a simulation of a universe with particular laws and initial conditions is contributing more to the measure of that possible universe than the random motions of molecules in a rock are contributing to its measure, since both can be seen as isomorphic to the events of that universe with the right mapping.

`Jesse Mazer`

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