I’m not thinking of it like specifying parts of the toy problem. I’m thinking of it as if for each of HM, TM, and TT, the observer is about to recieve 2 bits that describe which situation they’re in, and the only object that matters for the probability of each is the shortest program that reproduces all past observations plus the next 2 bits.
If we assume Sleeping Beauty has lots of information, we might expect that the shortest matching program will look like a simulation of physical law, plus a “bridging law” that, given this simulation, tells you what symbols get written to the tape. It is in this context that is seems like HM and TM are equally complex—you’re simulating the same chunk of universe and have what seems like (naively) a similar bridging law. It’s only for tuesday that you obviously need a different program to reproduce the data.
If we assume Sleeping Beauty has lots of information, we might expect that the shortest matching program will look like a simulation of physical law plus a “bridging law” that, given this simulation, tells you what symbols get written to the tape
I agree. I still think that the probabilities would be closer to 1⁄2, 1⁄4, 1⁄4. The bridging law could look like this: search over the universe for compact encodings of my memories so far, then see what is written next onto this encoding. In this case, it would take no more bits to specify waking up on Tuesday, because the memories are identical, in the same format, and just slightly later temporally.
In a naturalized setting, it seems like the tricky part would be getting the AIXI on Monday to care what happens after it goes to sleep. It ‘knows’ that it’s going to lose consciousness(it can see that its current memory encoding is going to be overwritten) so its next prediction is undetermined by its world-model. There is one program that will give it the reward of its successor then terminates, as I described above, but it’s not clear why the AIXI would favour that hypothesis. Maybe if it has been in situations involving memory-wiping before, or has observed other RO-AIXI’s in such situations.
I’m not thinking of it like specifying parts of the toy problem. I’m thinking of it as if for each of HM, TM, and TT, the observer is about to recieve 2 bits that describe which situation they’re in, and the only object that matters for the probability of each is the shortest program that reproduces all past observations plus the next 2 bits.
If we assume Sleeping Beauty has lots of information, we might expect that the shortest matching program will look like a simulation of physical law, plus a “bridging law” that, given this simulation, tells you what symbols get written to the tape. It is in this context that is seems like HM and TM are equally complex—you’re simulating the same chunk of universe and have what seems like (naively) a similar bridging law. It’s only for tuesday that you obviously need a different program to reproduce the data.
I agree. I still think that the probabilities would be closer to 1⁄2, 1⁄4, 1⁄4. The bridging law could look like this: search over the universe for compact encodings of my memories so far, then see what is written next onto this encoding. In this case, it would take no more bits to specify waking up on Tuesday, because the memories are identical, in the same format, and just slightly later temporally.
In a naturalized setting, it seems like the tricky part would be getting the AIXI on Monday to care what happens after it goes to sleep. It ‘knows’ that it’s going to lose consciousness(it can see that its current memory encoding is going to be overwritten) so its next prediction is undetermined by its world-model. There is one program that will give it the reward of its successor then terminates, as I described above, but it’s not clear why the AIXI would favour that hypothesis. Maybe if it has been in situations involving memory-wiping before, or has observed other RO-AIXI’s in such situations.