|Evolution is the key to understanding our nature.|
So the argument goes, once computers become sophisticated enough to simulate entire worlds, then lots of worlds will exist. Therefore, if there are many, many worlds, the chances of you happening to exist in "the real one" and not a simulation are very small.
I actually think the best answer to the idea that we might be living in a simulation comes from Wolfram. He was talking about weather predicting but it holds just as true for world creation. He points out that to fully simulate any system (e.g. a weather system) you need to simulate the quantum level, and that requires a simulation model exactly as complex as the system being simulated, and therefore at least as physically big as the system being simulated. This is because you can't simulate quantum systems with a smaller quantum system. If you could you would be relying on more subtle interactions, that also happen in the real system (and affect it) and therefore you would also need these in the simulation and can't use them to create the simulation.
So to simulate a universe requires something at least as big as a universe. The way round this is to cheat and not simulate all of the universe, but then you must have a universe with inconsistent physical laws (since some of the observable effects are not genuinely calculated but "fudged"). As far as we can tell our universe runs on consistent (but chaotic) laws, and is therefore probably not simulated.
The conclusion is that you can only fully simulate a closed system, because a simulation is a closed system. This is also, coincidentally, why weather forecasting will always suck.
However, David Cassandra Mertz asks:
"What if the real universe ribs much faster than the simulations, and we live in a timeshare slice of the simulator?"This does seem possible and quantized time might be an indication that this is the case. Potentially in "the real world" the speed of light is much higher, so the real quanta of time is smaller. A slower speed of light also makes the observable universe smaller - allowing a smaller universe to be simulated within the real one. However, it seems unlikely you'd have the physical space and energy to create "many worlds" this way.
As an interesting aside, computing speed doesn't matter. Time is only experienced by reality in frames (quanta) of the time it takes light to travel the shortest quantum distance, determined by Planck's constant. The unit of Planck Time is approximately 5.39 × 10−44 s. So even if it takes an hour, or a hundred years, for your computer to evaluate each frame the simulated world will still experience each frame sequentially and it will feel like "real time". The problem is physical space for state storage. Storing the state of a quantum system takes at least as much space as the "real" quantum system, you can't store the state (electronically, digitally or otherwise) in a smaller space. So to simulate a universe it requires a universe.
In the sense that reality is the product of collapsed probability waveforms, not resolved until observed (lazily evaluated), it could be said that the universe is already a simulation of itself. Every universe created (within the probably-not-real multiverse) is a new simulation.
"Imagine the best of all possible worlds. Now apply your will to making it happen. Magic is the product of will and imagination."