Boxing an AI is the idea that you can avoid the problems where an AI destroys the world by not giving it access to the world. For instance, you might give the AI access to the real world only through a chat terminal with a person, called the gatekeeper. This is should, theoretically prevent the AI from doing destructive stuff.
Eliezer has pointed out a problem with boxing AI: the AI might convince its gatekeeper to let it out. In order to prove this, he escaped from a simulated version of an AI box. Twice. That is somewhat unfortunate, because it means testing AI is a bit trickier.
However, I got an idea: why tell the AI it's in a box? Why not hook it up to a sufficiently advanced game, set up the correct reward channels and see what happens? Once you get the basics working, you can add more instances of the AI and see if they cooperate. This lets us adjust their morality until the AIs act sensibly. Then the AIs can't escape from the box because they don't know it's there.
Just... don't put it in a world where it should be able to upgrade infinitely? Make processors cost unobtainium and limit the amount of unobtainium so it can't upgrade past your practical processing capacity.
Remember that we are the ones who control how the box looks from inside.
Minor nitpick: if the AI finds itself in a box, I have to assume it will be let out. It's completely trivial to prevent it from escaping when not given help; the point in Eliezer's experiment is that the AI will be given help.
Note that this makes global processing power being limited evidence that the universe is a box.