John Collins writes: > I described a special case of this in a posting on this list a while > ago, suggesting that we're almost certainly not in a simulated, 'second > order' universe: Basically, for every arrangement of matter you could append > to our universe that would look like some creature controlling/observing us, > there would be many more arrangements that looked like no living creature.

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That's an interesting point, but I'm not sure it's correct. You might want to consider Nick Bostrom's "Simulation Argument" at www.simulation-argument.com as an alternative. 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. It seems plausible that our own laws of physics are not particularly complex. If string theory or loop quantum gravity or some other merging of QM and GR can work, we may well find that our entire universe is isomorphic to a few lines of mathematical equations. Similarly there are provocative hints that the initial state of the universe was extremely simple and had low complexity. These prospects lend support to my view, even though the universe contains objects of immense complexity. It's not the complexity of the universe that counts, it's the complexity of the equations that generate the universe. Consider a universe just like ours but where a given person is replaced by a random pattern of matter. Based on matter complexity, such a universe may seem more likely, since the structure of a human being is incredibly complex. But based on generative-law complexity, such a universe is much less likely, since it has a "hole" where the laws of physics did not apply, where what should have been a human being was artificially replaced by a random pattern. 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). Nick Bostrom proposes in effect that the outer universe could be the mathematically identical to the inner one. He also suggests that there could be many simulations running, so that the number of observers in the simulated universes is far greater than the number in the outer universe. Based on this reasoning, the likelihood of our being in a second-order simulated universe is very considerable and can't be ruled out. Hal Finney