Adding a universe external to this one doesn't just add more stuff.
The SA does not 'add' a universe external to the model. The SA is a deduction derived from the Singularity-model. The Singularity-model does not 'add' the external universes either, they emerge within it naturally, just as naturally as future AI's do.
For the inhabitants, a model that not only explained how their universe worked, but postulated the existence of our universe, would be more complex than one that merely explained their own.
That would only be true if their model was not also a full explanation of our universe, and thus isomorphic to some historical slice of our universe.
In terms of minimum message length, having to describe another universe superordinate to your own adds to the information of the model,
Not at all. The Singularity-model is a scientific extrapolation of our observed history into the future. As it is scientific, it reduces to physics (the model approximates what we believe would happen if we could simulate physics into the future).
The SA is not a model at all. It is a deduction which can be simplified down to:
If the Singularity-model is accurate.
Then most observable universes are simulations.
And thus our observable universe is a simulation.
You seem to think the minimum message length is somehow physics + extra simulations scrawled in. The physics generates everything, so it's already minimal.
The addition of our own universe could not be encapsulated in a model that simply describes the working of the simulated Conway universe from the inside without adding more information.
No - but only because the physics differ substantially. You are right of course that if Conway beings evolved and somehow they had some singularity of their own in their future that generated simulated Conway universes, they would establish a lower prior to believing they were embedded in a String/M-theory universe like ours. (they of course could still be wrong, as complexity is just a reasonable bias measure). They'd attach higher credence to being embedded in a Conway universe.
But if the simulated universe is based on the same physics, then it reduces to exactly the same minimal program, and it absolutely describes both universes.
This is very similar to the multiverse in physics and the space of universes string/M-whatever theory can generate.
As I mentioned before, I thought you were arguing the orthodox simulation argument, rather than one where the simulations are created from within our own universe. That would not necessarily increase the complexity of the model, but it's untenable for its own reasons.
For one thing, it's far from given that any civilization would ever want to simulate the universe at a previous point; the reasons you provided before don't remotely justify such a project; it's not a practical use of computing power. For another, assuming you're only simulating small fractio...
Many folk here on LW take the simulation argument (in its more general forms) seriously. Many others take Singularitarianism1 seriously. Still others take Tegmark cosmology (and related big universe hypotheses) seriously. But then I see them proceed to self-describe as atheist (instead of omnitheist, theist, deist, having a predictive distribution over states of religious belief, et cetera), and many tend to be overtly dismissive of theism. Is this signalling cultural affiliation, an attempt to communicate a point estimate, or what?
I am especially confused that the theism/atheism debate is considered a closed question on Less Wrong. Eliezer's reformulations of the Problem of Evil in terms of Fun Theory provided a fresh look at theodicy, but I do not find those arguments conclusive. A look at Luke Muehlhauser's blog surprised me; the arguments against theism are just not nearly as convincing as I'd been brought up to believe2, nor nearly convincing enough to cause what I saw as massive overconfidence on the part of most atheists, aspiring rationalists or no.
It may be that theism is in the class of hypotheses that we have yet to develop a strong enough practice of rationality to handle, even if the hypothesis has non-negligible probability given our best understanding of the evidence. We are becoming adept at wielding Occam's razor, but it may be that we are still too foolhardy to wield Solomonoff's lightsaber Tegmark's Black Blade of Disaster without chopping off our own arm. The literature on cognitive biases gives us every reason to believe we are poorly equipped to reason about infinite cosmology, decision theory, the motives of superintelligences, or our place in the universe.
Due to these considerations, it is unclear if we should go ahead doing the equivalent of philosoraptorizing amidst these poorly asked questions so far outside the realm of science. This is not the sort of domain where one should tread if one is feeling insecure in one's sanity, and it is possible that no one should tread here. Human philosophers are probably not as good at philosophy as hypothetical Friendly AI philosophers (though we've seen in the cases of decision theory and utility functions that not everything can be left for the AI to solve). I don't want to stress your epistemology too much, since it's not like your immortal soul3 matters very much. Does it?
Added: By theism I do not mean the hypothesis that Jehovah created the universe. (Well, mostly.) I am talking about the possibility of agenty processes in general creating this universe, as opposed to impersonal math-like processes like cosmological natural selection.
Added: The answer to the question raised by the post is "Yes, theism is wrong, and we don't have good words for the thing that looks a lot like theism but has less unfortunate connotations, but we do know that calling it theism would be stupid." As to whether this universe gets most of its reality fluid from agenty creators... perhaps we will come back to that argument on a day with less distracting terminology on the table.
1 Of either the 'AI-go-FOOM' or 'someday we'll be able to do lots of brain emulations' variety.
2 I was never a theist, and only recently began to question some old assumptions about the likelihood of various Creators. This perhaps either lends credibility to my interest, or lends credibility to the idea that I'm insane.
3 Or the set of things that would have been translated to Archimedes by the Chronophone as the equivalent of an immortal soul (id est, whatever concept ends up being actually significant).