A special case of this is dealing with the locations of things. A computer monitor displays information in pixels which form in nice neat rows and columns. You can put a dot "on" a pixel; but you can't actually put a dot in between pixels. Now there's a technique (technical term: anti-aliasing); where you spread the dot out in a statistical manner. So if you want it to be on the line in between two pixels, you put 50% of its color in one pixel and 50% in the other. The idea is that when the human eye looks at that from a distance, it will average things out and make you think that the dot is in between when it isn't. Now pixels are 2 dimensional concepts, but there is a 3 dimensional equivalent: voxels, and they have the same issue – there is a smallest unit of position and the only way to fake that out is to spread the location of things over several voxels.

Second, digital computers work using a finite clock speed. That's what all the Megahertz and Gigahertz talk is all about – it takes time for computers to do something. In simulations this means that you take the information about where everything is "now" and then calculate where everything will be in some small amount of time later. The result is that in computer simulations, time jumps in steps – there is a smallest unit of time (just as there is a smallest unit of everything else). Game players know this as the "frame rate" problem – that because it takes time to do all of this calculation, the computer can only update the screen a limited number of times a second. If that "frame rate" is high enough, you never notice (televisions in the use a frame rate of 60 times a second, and few people notice); but if the frame rate gets down to 5-10, it becomes impossible to play some games. Now if we all live in a computer simulation, its would seem that the frame rate is fairly high; but still if you look at things happening fast enough, you would expect to find sudden jumps in time.

Third, digital computers themselves are finite, and therefore can not be used to actually simulate an infinite universe. Game developers face the same problem – how to keep players from "walking off the edge of the map" and ruining the illusion of the simulation. Many resort to brute force solution – building impassable walls in the games that keep the players in the area that is simulated. Others are more creative – they leave the illusion that you could just walk in one direction forever; but make the journey impractical. Now if we are all in a computer simulation, it's clear the author(s) of that simulation want us to believe the universe is infinite (or at least very large), so we would expect to find some means to dissuade us from heading off in one direction and finding the edge of the simulation.

So how does the world we live in stack up?

Well, Quantum Mechanics says that all of the key pieces of information in the universe – energy, change, spin, etc. are all "quantized" – they all have some smallest unit, and it is impossible to have smaller that that unit. When you get down into small energies and small charges, you see these big jumps from 1 to 2 to 3. Exactly what you'd expect if we were living in a computer simulation.

Furthermore, the latest attempts at a "Grand Unified Theory" in physics (a "Theory of Everything") – theories like Quantum Loop Gravity, specify that space and time are also quantized. That there is a smallest unit of distance and of time – just as you would expect in a computer simulation. But even without resorting to the latest theories (which are far from proven), basic quantum mechanics says that things typically don't have precise positions – they tend to be spread out probabilistically over several locations – just like anti-aliasing pixels or voxels.

Finally – what about some way to keep us from realizing the simulation is limited? Well, The theory of Relativity puts an upper bound of how fast we can move, and in fact makes it infinitely costly to go even that fast. Because of relativity, travel outsize of our solar system is going to be a very slow process, and communication with anyone doing it will be limited and slow. An excellent solution if you ask me. It discourages anyone from trying, and if someone tries, you have the time to set up a separate simulation for the traveler and have opportunity to control the communication between the simulations.

Interesting eh?

To be completely clear, I do NOT believe that this is the case. However, I have to admit that there is nothing about this scenario which actually contradicts anything which I do believe, and as a software engineer I find the idea that God may also be a software engineer (and a pretty impressive one at that) strangely comforting.