I remember seeing The Matrix for the first time, having no prior knowledge of the movie, and coming out of it thinking: "A big budget Hollywood movie about epistemology! How cool is that?!" Now the image of the Matrix is such a commonplace that philosophers have started using it, at least as a pedagogical tool, as in this game on the Philosophers Magazine website, and on Thoughts, Arguments, and Rants (look at the entry for Sunday). There are even two different books on the subject: The Matrix and Philosophy: Welcome to the Desert of the Real and Taking the Red Pill: Science, Philosophy and Religion in The Matrix. Apparently there was also a post on the 617 blog about multi-level Matrices, but unfortunately as I write this their archives are unavailable, so I don't know if it has anything to do with what I'm going to talk about.
The basic Matrix argument is that a) you cannot be sure that every experience you have is not a perfect computer simulation and b) this is a live possibility in a way that , say, pure solipsism or the theory that there's an intangible invisible imp on your shoulder is not, in that there is a possible experience you could have which would tend to confirm it: to whit, being unplugged from the Matrix. Of course, the same argument applies to the world outside of the Matrix: the people who unplugged you face the same possibility that they and you are in a higher-level Matrix, which could be confirmed by being unplugged. Obviously this leads to an infinite regress of suppositions, but that doesn't mean it's wrong.
What I would like to consider is the Matrix scenario with a twist: Upon being unplugged from the Matrix, when the unpluggers tell you "Welcome to the Desert of the Real," you respond:
"What do you mean, real? This world that you call real is itself a computer simulation. When you attempt to look in on the Matrix, you're actually being fed images from the real world, where I come from; when you decided to 'unplug' me, I was plugged into your Matrix. Of course, they gave me a drug to erase my short term memory of the experience of being plugged in, so that there's no difference between my memories and what you think my memories ought to be, but there is an experience that either of us could have which would tend to confirm the truth of what I say: being unplugged."
The question about this account is not whether it is plausible (I should hope not), but whether the unpluggers would have any better reason to discount the possibility than we have of discounting the possibility of the Matrix? I don't think so; it has what appear to me to be the same salient features: it perfectly explains what experiences we do have, while suggesting an experience that we could conceivably have which would tend to confirm the theory that they were merely simulated (granted, without closing down the possibility of further experiences that might modify the conclusion). I call this the Moebius matrix because it's (very loosely) a one-sided loop: there's only one reality, despite the two apparent sides, and if you accept the argument then the "real" world is always the one that your consciousness is not currently aware of.