Despite the title, this blog post is really here as a warning to others about trying to reason from first principles about the nature of our Universe...
We have already done sophisticated simulations ourselves that do the large scale simulation of structure in our Universe. Yes, this is for a small fraction of the total Universe, and, yes, it only simulates down to galaxy size. (That is, it doesn't simulate small enough areas to model the formation of stars or anything like that.) But the point remains that we're simulating the Universe.
We've also done "artificial life" simulations, in which we've shown that computer programs evolve. One of the most interesting physics colloquia I heard as a grad student at Caltech in the first half of the 1990's was about the Tierra project, that created an "environment" in which small computer programs competed for resources. It had a mechanism for random mutation, and over time the programs evolved to become more efficient.
Take these simulations, and allow for computer power to continue to improve as we've seen it improving in recent decades, and it really doesn't seem too much of a stretch to imagine that we could create a simulation of the local area of a galaxy that has the computer power necessary to evolve very complex "organisms"-- simulated organisms, that is. Code in the basic laws of physics, and give them enough space and computer power to evolve, and it could just happen.
Now, consider our Universe as we've observed it to be. We only know of one life-bearing planet, but we do know that there are lots of other planets in our Galaxy. And, looking out there, within the observable Universe (not even considering things so far away that light hasn't had time to reach us since the Big Bang), there are something like 100 billion galaxies like ours. Given how tenacious life is on this planet once it got started, even if it's rare for it to get started (say even only one or a few instances in our own Galaxy), there are certainly other planets out there with life on them.
If we use our statistical sample size of one, so far we see that a few hundred years out of a few billion years of evolution includes a technological civilization. That's a small fraction... but given the number of stars in our Galaxy, and the number of galaxies in the observable Universe, it means that there are other technological civilizations out there, somewhere. Let's assume that an appreciable fraction (i.e. anything more than an infinitesimal fraction) of these civilizations eventually are able to produce computation able to make the kinds of simulations I'm talking about above. It's been for the last 7 billion years or so that it's reasonable to suppose that life could arise on planets like our own. During those 7 billion years, there have almost certainly been lots of these simulations run. (What does "lots" mean? Well, the numbers going into this are very uncertain, of course, but it's probably somewhere between hundreds and billions.)
In other words: for one observable Universe like our own, in which intelligent creatures could arise, there are many simulations in which intelligent creatures could arise. Thus, any given civilization of intelligent creatures is by far more likely to be within one of the simulations rather than in the real Universe.
So, we're probably all part of somebody's simulation.
Right. Do I really believe that? No. I mean, maybe, but if so, so what?. If the simulation were done well enough, though, we'd have no way to tell the difference. So, at some level, trying to decide if we're somebody's civilization or if we're in a real Universe is mental masturbation. We see a Universe out there which has physical laws that are Universally obeyed. The process of science has a great track record in explaining how this Universe works and predicting what we will observe. Hence, it makes the most sense to go with the simplest explanation, that there is a real Universe and we are working on understanding it. If certain things about our Universe seem improbable from first principles-- for instance, why are the densities of Dark Matter and Dark Energy so close?-- it's worth thinking about whether that's a pointer to something deeper. But, at some level, the Universe is what it is, and it's worth trying to understand it without getting hung up on fundamental probabilistic arguments that lead us to thinking that none of it means anything anyway.