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.

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

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