The Simulation Argument

It goes like this: "Pretty soon we're going to have really powerful computers. One of the things that people will want to do with these really powerful computers is run simulations--simulations of their own societies. Then those simulations will probably also want to run simulations! And so on. In fact, there will likely be far, far more simulated people than actual people. Wait, did I say 'will?' I meant are. Yeah, it's statistically likely that it's happening right now, and we're the simulations."

The problem I have with that is this: how can you build a computer that can simulate the existence of (as many or) more molecules than are used to build the computer? Electro-magnetic, weak nuclear, strong nuclear, gravitic forces would all have to be simulated, and the number of calculations necessary to work all that math out for a single molecule would almost certainly take more than one molecule. Take the gravitic force in particular--gravitic force extends over a monstrously huge area, so that every molecule in the entire Earth exerts a gravitic effect on every other--every molecule in the solar system, every molecule in the galaxy, every molecule in the universe. Simply working out the gravitic interactions in my left hand could take a solar system's weight in computronium.

Assuming that we are ourselves a simulation, that leaves two possibilities. Either our experience of the universe is semi-illusory, and individual atoms don't actually exist unless unless they have to in order to maintain the illusion. (Wouldn't that be an interesting explanation for the wave/particle duality!) Or alternatively, the laws of physics in our universe are grossly simplified versions of those in the simulating universe.

Now, step two of the simulation argument is that the simulations will probably run simulations of their own. So what happens if we, semi-illusory/drastically simplified simu-verse, try to run our own simulation? Either we build a computer according to the faked laws of physics and, unable to pull off a simulated quantum computer, our universe crashes. Or we are forced to simplify the governing laws of our own simulation, either by making it much smaller molecule-wise than our own, or by faking some stuff.

Imagine matrioshka dolls (those Russian nesting dolls): just as each one is smaller than the one that contains it, so too is each simulation smaller than its progenitor. Depending on how efficiently universes can be simulated, each one may be vastly smaller--an order of magnitude smaller or more. If this number is large enough, it can very much bork the entire premise.