Ironically, maybe the problem is that even if this is not specific enough. I am somewhat (but not entirely) confident that when we talk about ‘what AIXI would do’, we have to check that all AIXI instantiations would indeed do the same thing; if not, we have to pick which similar (in whatever respect) instantiations we’re referring to and go from there. The formal specification of AIXI does not specify what would happen if a light/the lights go out (if an anvil is dropped). An AIXI instantiation in one world might lose a camera and be left to fend for itself; in another world, Omega appears and replaces the camera. An operating system might make no mention of peripherals being removed, but the behaviour of the computer it is installed on (e.g. what signals, if any, the hardware sends to the operating system when a peripheral is removed) can affect its inputs.
What would a decision algorithm that acted depending on its specific instantiation look like? I guess a voice recorder could, using a suitable recording, be made to say, “I have buttons composed of atoms, and this playback is causing slight perturbations of those buttons and myself at this very moment.” But tape recorders in universes without atoms could be made to say that, too, so the tape recorder would not actually be sensitive to the type of world in which it’s actually embedded. For a finite set of simple universes, we might be able to specify a machine, whose algorithm we know, that can identify which of those universes it’s in. (Arguably for a non-finite set, humans can sort of do this; though we don’t know how they work or what we might call their algorithms.) But would it be possible to prove that the algorithm does so without hard-coding a bunch of if statements into it? Maybe this is another ‘how much can we leave to the FAI, and how much can we trust its work without checking it ourselves’ thing?
I’m not sure what you’re trying to say when talking about many instantiations. I am imagining all the extant machines synchronise their inputs and so there is only one AIXI instance. The input is some kind of concatenation of the sensory inputs of all of the machines with some kind of blank for nonfunctioning sensors. If I also considered scenarios where the communication lines can be cut the agent would be forced to split into more than one instance, and then it would not be so clear how or weather the agent can learn the reasonable intelligent behavior, which is why I did not consider that.
Ironically, maybe the problem is that even if this is not specific enough. I am somewhat (but not entirely) confident that when we talk about ‘what AIXI would do’, we have to check that all AIXI instantiations would indeed do the same thing; if not, we have to pick which similar (in whatever respect) instantiations we’re referring to and go from there. The formal specification of AIXI does not specify what would happen if a light/the lights go out (if an anvil is dropped). An AIXI instantiation in one world might lose a camera and be left to fend for itself; in another world, Omega appears and replaces the camera. An operating system might make no mention of peripherals being removed, but the behaviour of the computer it is installed on (e.g. what signals, if any, the hardware sends to the operating system when a peripheral is removed) can affect its inputs.
What would a decision algorithm that acted depending on its specific instantiation look like? I guess a voice recorder could, using a suitable recording, be made to say, “I have buttons composed of atoms, and this playback is causing slight perturbations of those buttons and myself at this very moment.” But tape recorders in universes without atoms could be made to say that, too, so the tape recorder would not actually be sensitive to the type of world in which it’s actually embedded. For a finite set of simple universes, we might be able to specify a machine, whose algorithm we know, that can identify which of those universes it’s in. (Arguably for a non-finite set, humans can sort of do this; though we don’t know how they work or what we might call their algorithms.) But would it be possible to prove that the algorithm does so without hard-coding a bunch of if statements into it? Maybe this is another ‘how much can we leave to the FAI, and how much can we trust its work without checking it ourselves’ thing?
I’m not sure what you’re trying to say when talking about many instantiations. I am imagining all the extant machines synchronise their inputs and so there is only one AIXI instance. The input is some kind of concatenation of the sensory inputs of all of the machines with some kind of blank for nonfunctioning sensors. If I also considered scenarios where the communication lines can be cut the agent would be forced to split into more than one instance, and then it would not be so clear how or weather the agent can learn the reasonable intelligent behavior, which is why I did not consider that.