Why couldn’t two identical AIXI-type agents recognize one another to some extent? Stick a camera on the agents, put them in front of mirrors and have them wiggle their actuators, make a smiley face light up whenever they get rewarded. Then put them in a room with each other.
If you’re suggesting this as a way around AIXI’s immortality delusion, I don’t think it works. AIXI “A” doesn’t learn of death even if it witnesses the destruction of its twin, “B”, because the destruction of B does not cause A’s input stream to terminate. It’s just a new input, no different in kind than any other. If you’re considering AIXI(tl) twins instead, there’s also the problem that an full model of an AIXI(tl) can’t fit into its own hypothesis space, and thus a duplicate can’t either.
Lots of humans believe themselves to be Cartesian, after all, and manage to generalize from others without too much trouble. “Other humans” isn’t in a typical human’s hypothesis space either — at least not until after a few years of experience.
AIXI doesn’t just believe it’s Cartesian. It’s structurally unable to believe otherwise. That may not be true of humans.
Xia: But the 0, 0, 0, … is enough! You’ve now conceded a case where an endless null output seems very likely, from the perspective of a Solomonoff inductor. Surely at least some cases of death can be treated the same way, as more complicated series that zero in on a null output and then yield a null output.
Rob: There’s no reason to expect AIXI’s whole series of experiences, up to the moment it jumps off a cliff, to look anything like 12, 10, 8, 6, 4. By the time AIXI gets to the cliff, its past observations and rewards will be a hugely complicated mesh of memories. In the past, observed sequences of 0s have always eventually given way to a 1. In the past, punishments have always eventually ceased. It’s exceedingly unlikely that the simplest Turing machine predicting all those intricate ups and downs will then happen to predict eternal, irrevocable 0 after the cliff jump.
Put multiple AIXItI’s in a room together, and give them some sort of input jack to observe each other’s observation/reward sequences. Similarly equip them with cameras and mirrors so that they can see themselves. Maybe it’ll take years, but it seems plausible to me that after enough time, one of them could develop a world-model that contains it as an embodied agent.
I.e. it’s plausible to me that an AIXItI under those circumstances would think: “the turing machines with smallest complexity which generate BOTH my observations of those things over there that walk like me and talk like me AND my own observations and rewards, are the ones that compute me in the same way that they compute those things over there”.
After which point, drop an anvil on one of the machines, let the others plug into it and read a garbage observation/reward sequence. AIXItI thinks, “If I’m computed in the same way that those other machines are computed, and an anvil causes garbage observation and reward, I’d better stay away from anvils”.
If you’re suggesting this as a way around AIXI’s immortality delusion, I don’t think it works. AIXI “A” doesn’t learn of death even if it witnesses the destruction of its twin, “B”, because the destruction of B does not cause A’s input stream to terminate. It’s just a new input, no different in kind than any other. If you’re considering AIXI(tl) twins instead, there’s also the problem that an full model of an AIXI(tl) can’t fit into its own hypothesis space, and thus a duplicate can’t either.
AIXI doesn’t just believe it’s Cartesian. It’s structurally unable to believe otherwise. That may not be true of humans.
Let me try to strengthen my objection.
Put multiple AIXItI’s in a room together, and give them some sort of input jack to observe each other’s observation/reward sequences. Similarly equip them with cameras and mirrors so that they can see themselves. Maybe it’ll take years, but it seems plausible to me that after enough time, one of them could develop a world-model that contains it as an embodied agent.
I.e. it’s plausible to me that an AIXItI under those circumstances would think: “the turing machines with smallest complexity which generate BOTH my observations of those things over there that walk like me and talk like me AND my own observations and rewards, are the ones that compute me in the same way that they compute those things over there”.
After which point, drop an anvil on one of the machines, let the others plug into it and read a garbage observation/reward sequence. AIXItI thinks, “If I’m computed in the same way that those other machines are computed, and an anvil causes garbage observation and reward, I’d better stay away from anvils”.